Solving Percent Problems Word Problems Find a Pattern Estimation - - PDF document

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Solving Word Problems

Pre-Algebra Slide 2 / 142

Rate Problems Combination Problems Find a Pattern Geometry Problems Percent Problems Estimation Problems Fraction Problems LCM / GCF Problems Proportion Problems Integer Operations Problems Order of Operation Problems

Table of Contents

Strategies & Plans for Problem Solving

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Strategies & Plans for Problem Solving

Return to Table of Contents

Slide 4 / 142 Problem Solving Strategies

Most problems can be solved by incorporating one or more strategies. Work backwards Make a table, chart or diagram Solve a simpler or similar problem Guess and check Look for a pattern Eliminate possibilities Draw a picture

Slide 5 / 142 Plan for Solving a Word Problem

Plan: Read the problem several times. What do you know? What do you need to find? Eliminate any unnecessary information. Set Up: Define a variable. Making a chart or drawing a picture may be helpful. Write an open sentence. Solve the open sentence.

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Check: Reread the problem. Did you answer the question? Did you state your answer clearly with the appropriate units? Is your answer consistent with the information given in the problem?

Plan for Solving a Word Problem

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Rate Problems

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How many miles did he ride the bicycle? Tim ran on the elliptical for 1.6 hours at a speed of 11.4 miles per hour. How many miles did she ride the bicycle? Tim ran for 1.6 hours. His speed was 11.4 miles per hour. What do you know? What is the question to be answered?

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18.24 miles Distance = Rate Time What does this remind you of? Solve the problem and check here for the answer. Tim ran on the elliptical for 1.6 hours at a speed of 11.4 miles per hour. How many miles did she ride the bicycle?

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How many customers can be served in an hour? A grocery store checker can total the purchases for 3 customers in 10 minutes. At this rate, how many customers can the checker serve in one hour? Checker can serve 3 customers in 10 minutes. What do you know? What is the question to be answered?

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18 customers A grocery store checker can total the purchases for 3 customers in 10 minutes. At this rate, how many customers can the checker serve in one hour? Distance = Rate Time What does this remind you of? Solve the problem and check here for the answer.

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1 You run at a speed of 8.5 minutes per mile. How long does it take to run 7 miles?

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2 You run at a speed of 8.5 minutes per mile. How many miles per hour do you run?

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3 If you are driving at 45 miles per hour, how far can you go in 3.5 hours?

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4 If you are driving at 65 miles per hour, about how long does it take to travel 309 miles?

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5 You can fill 8 bags of sand every 3 minutes. How long does it take to fill 20 bags?

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Percent Problems

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How much is the tip? The total bill is $82.97. The tip should be 15% of that total. In a restaurant, it is customary to leave a 15% tip.

• A. How much money should you leave as

a tip if the bill for your party comes to $82.97? Note: For the purposes of instruction, "pin" this page while working through Parts A and B of this question. What do you know? What is the question to be answered?

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$12.45 Find 15% of $82.97. In a restaurant, it is customary to leave a 15% tip.

• A. How much money should you leave as

a tip if the bill for your party comes to $82.97? Solve the problem and check here for the answer. What will you do to find the solution?

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What is the difference between a 15% and an 18% tip? The total bill is $82.97. The tip should be 18% of that total.

• B. If there are 6 or more people in your party,

the restaurant requires you to leave an 18%

• tip. What would be the difference in the tip

amount if there were 6 people rather than 4 people in your party? What do you know? What is the question to be answered?

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$2.48 Find 18% of $82.97 and subtract $12.45.

• B. If there are 6 or more people in your party,

the restaurant requires you to leave an 18%

• tip. What would be the difference in the tip

amount if there were 6 people rather than 4 people in your party? What will you do to find the solution? Solve the problem and check here for the answer.

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As a sales rep, you earn 15% commission on your monthly sales. If your total sales last month was $2,750 how much do you earn?

Do? Solution

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When waiting tables, you can expect to earn 18% of the bill as a tip. The total bills for one night is $960. How much can you expect to earn if you need to tip out the

• ther workers at 5%?

Solution Do?

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6 How much tip should you leave a waitress for a $130 bill? Her service was good so you want to leave 18%.

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7 What is the tax on a $285 purchase? Tax is 7%.

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8 How much will you earn in commission if you sell $2,400 worth of merchandise and your commission is 12%?

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9 You did not pay your bill on time. There is a 24% finance

• charge. If the original bill was $5,250 what is the new

amount due?

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10 As a waiter, how much can you expect to earn if the total for the night's bills is $950? Standard 18% tipping applies.

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Find a Pattern

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What are the next three numbers in the pattern: 2, 3 1/4, 4.5, 5 3/4, __, __, __ ? Answers: 7, 8 1/4 or 8.25, 9.5 or 9 1/2

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Audrey's Pattern Bjorn's Pattern Clara's Pattern 2 2 2 4 4 4 6 8 16 Audrey, Bjorn, and Clara each began to write a number pattern for a class assignment. Their patterns are shown in the table below. Note: For the purposes of instruction, "pin" this page while working through Parts A, B, and C of this question.

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1 x 2 = 2 2 2 x 2 = 4 or 2 + 2 3 x 2 = 6 4 + 2 Part A. Complete Audrey's pattern by writing four more numbers in the table. Explain the rule for her pattern. What are the next four numbers in the pattern? What do you know? What is the question to be answered?

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x 2 or +2 each step 8 10 12 14 Continue the pattern four more times. Part A. Complete Audrey's pattern by writing four more numbers in the table. Explain the rule for her pattern. What will you do to find the solution? Solve the problem and check here for the answer. Explain the rule for the pattern.

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What are the next three numbers in the pattern? 21 = 2 2 22 = 4 or 2 x 2 2

3 = 8 4 x 2

Part B. Complete Bjorn's pattern by writing three more numbers in the table. Explain the rule for his pattern. What do you know? What is the question to be answered?

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2x or 2x2=4 4x4=16 16 32 64 Continue the pattern three more times. Part B. Complete Bjorn's pattern by writing three more numbers in the table. Explain the rule for his pattern.

What will you do to find the solution? Solve the problem and check here for the answer. Explain the rule for the pattern.

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What are the next two numbers in the pattern? 2 2

2 = 4

42 = 16 Part C. Complete Clara's pattern by writing two more numbers in the table. Explain the rule for her pattern. Source: Learnia What do you know? What is the question to be answered?

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256 65,536 2x2 = 4 4x4 = 16 16x16 = 256 Continue the pattern two more times. Part C. Complete Clara's pattern by writing two more numbers in the table. Explain the rule for her pattern.

What will you do to find the solution? Solve the problem and check here for the answer. Explain the rule for the pattern.

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Some cows and chickens live on a farm. The total number of their legs is 48 and the total number of heads is 17. How many cows live on the farm? Answer: 7 cows.

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The Fibonacci Sequence is a repeating pattern found in

• nature. Study the sequence and find the next two

terms. 0, 1, 1, 2, 3, 5, 8, 13, 21, 33, 54, ___, ___ Answer: Next term is sum of two previous terms. 87, 141

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11 Find the next number in the sequence.

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Estimation Problems

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There are 32 members in the Quilting Club. Each member decorated a fabric square that measured 7 inches on each

• side. The members then sewed the fabric squares together

to make a quilt. John estimated that the area of the finished quilt is about 1500 square inches. Note: For the purposes of instruction, "pin" this page while working through Parts A, B, and C of this question.

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What is the area of each fabric square? Each fabric square measured 7 inches on a side. Part A. What is the area of each fabric square? Show your work or explain how you got your answer. What do you know? What is the question to be answered?

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49 in2 Use the formula A = s s or A = s2 Part A. What is the area of each fabric square? Show your work or explain how you got your answer. What will you do to find the solution? Solve the problem and check here for the answer.

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What expression estimates the area of the quilt? Each square is 7 in on a side. There are 32 members. Part B. Write an expression that can be used to estimate the area of the finished quilt. What do you know? What is the question to be answered?

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30 x 50 Estimate 32 squares as 30 squares and 49 in2 as 50 in2. Part B. Write an expression that can be used to estimate the area of the finished quilt. What will you do to find the solution? Solve the problem and check here for the answer.

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Is John's estimate reasonable? The area of each square is 49 in2. There are 32 squares. Part C. Is John's estimate reasonable? Explain why or why not. What do you know? What is the question to be answered?

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Actual area is 1568 in2. Yes, it is reasonable. Compare John's estimate to the actual area. Part C. Is John's estimate reasonable? Explain why or why not. What will you do to find the solution? Solve the problem and check here for the answer.

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Sue paid $3.78 for a package of 10 hot dogs and $1.15 for a package of 8 hot dog buns. She estimated that the combination of 1 hot dog and 1 hot dog bun would cost about 50 cents. Note: For the purposes of instruction, "pin" this page while working through Parts A, B, and C of this question.

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What is the estimated cost of 1 hot dog? Hot dogs are sold in a pack of 10 for $3.78 Part A. Estimate the cost of 1 hot dog. Show your work or explain your answer. What do you know? What is the question to be answered?

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$0.40 for one hot dog Round $3.78 to $4.00 and divide by 10 Part A. Estimate the cost of 1 hot dog. Show your work or explain your answer. What will you do to find the solution? Solve the problem and check here for the answer.

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What is the estimated cost of 1 bun? Buns are sold in a pack of 8 for $1.15 Part B. Estimate the cost of 1 hot dog bun. Show your work or explain your answer. What do you know? What is the question to be answered?

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$0.10 for one hot dog bun Round $1.15 to $1.00; round 8 to 10 and divide. Part B. Estimate the cost of 1 hot dog bun. Show your work or explain your answer. What will you do to find the solution? Solve the problem and check here for the answer.

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Is $0.50 a reasonable estimate for at hot dog and bun? Estimated costs of a hot dog is $0.40 and of a bun is $0.10 Part C. Explain why Sue's estimate is reasonable or unreasonable. What do you know? What is the question to be answered?

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It is reasonable. We rounded both costs down. Compare your answer to Sue's estimate. Part C. Explain why Sue's estimate is reasonable or unreasonable. What will you do to find the solution? Solve the problem and check here for the answer.

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16 Janice wants to buy two speakers for her computer. Each speaker costs $69.95. If Janice has $135, can she afford to buy the speakers?

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17 A truck contains 3,000 pounds of asphalt. The crew needs to pave an area 3.5 yards wide and 4.75 yards long. Do they have enough asphalt?

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18 The middle school needs nine buses to serve its students. The buses travel a total of 4,586 miles in one week. About how many miles does each bus travel in one week?

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19 A stadium holds 12,000 people. If the bleachers hold 3,856 people, about how many seats are in the rest of the stadium?

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20 Your high school collected canned goods. The Freshman Class collected 2,678 cans, the Sophmore class collected 2,874 cans, the Junior Class collected 4,657 cans and the Senior Class collected 3,341 cans. The school newspaper reported that over 13,000 cans were collected. Is this reasonable?

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Fraction Problems

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If the average 11 year old can eat 3/8 of a pizza, how many 11 year olds can 5 1/2 pizzas feed? Answer: 5 1/2 = 44/8 so, 44/3 = approximately 14 or 15 11 year olds

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There are 24 students in Mrs. Smith's class. If 2/3 of the students are girls, how many are boys? Answer: 8 boys. 2/3 of the students is 16.

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Sarah, Tom, Juan and Margo are team leaders for their class in their Box Tops collection contest. Sarah's team collected 60 Box Tops. Tom's team collected 35 Box

• Tops. Juan's team collected 50 Box Tops and Margo's

team collected 55 Box Tops. How many Box Tops did they collect altogether? What fraction of the total did Sarah's team collect? Juan's? Margo's? Note: For the purposes of instruction, "pin" this page while working through Parts A, B, C and D of this question.

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How many Tops did they collect altogether? Sarah - 60 Tops Tom - 35 Tops Juan - 50 Tops Margo - 55 Tops Part A. How many Box Tops did they collect in their contest altogether? What do you know? What is the question to be answered?

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200 Box Tops Altogether means "add." Part A. How many Box Tops did they collect in their contest altogether? What will you do to find the solution? Solve the problem and check here for the answer.

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What fraction of the total did Sarah's team collect? Sarah collected 60 Tops A total of 200 Tops were collected. Part B. What fraction of the total did Sarah's team collect? What do you know? What is the question to be answered?

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Numerator = Sarah's total Denominator = 200 Part B. What fraction of the total did Sarah's team collect? 3 10 What will you do to find the solution? Solve the problem and check here for the answer.

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What fraction of the total did Juan's team collect? Juan collected 50 Tops. A total of 200 Tops were collected. Part C. What fraction of the total did Juan's team collect? What do you know? What is the question to be answered?

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Numerator = Juan's total Denominator = 200 Part C. What fraction of the total did Juan's team collect? 1 4 What will you do to find the solution? Solve the problem and check here for the answer.

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What fraction of the total did Margo's team collect? Margo collected 55 Tops. A total of 200 Tops were collected. Part D. What fraction of the total did Margo's team collect? What do you know? What is the question to be answered?

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Numerator = Margo's total Denominator = 200 Part D. What fraction of the total did Margo's team collect? What will you do to find the solution? 11 40 Solve the problem and check here for the answer.

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How many cups of oil will she need? A recipe calls for 3/8 cup of oil. Ann wants to make 1 1/2 times as many muffins. A muffin recipe calls for 3/8 cup of oil. Ann wants to make 1 1/2 times the number of muffins in one recipe. How many cups of oil will she need? What do you know? What is the question to be answered?

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cup 9 16 "times" means multiplication A muffin recipe calls for 3/8 cup of oil. Ann wants to make 1 1/2 times the number of muffins in one recipe. How many cups of oil will she need? What will you do to find the solution? Solve the problem and check here for the answer.

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21 You have a dump truck full of driveway stones. You start with 2 tons of stones. At your first stop, you deliver half the stones. At your second stop, you deliver 1/3 of the remaining stones. At your third stop, you deliver 1/4 of the remaining stones. What fraction of the stones are left?

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22 You are baking cookies and want to make a third batch of batter. If the recipe calls for 2 1/4 cups of flour, how much will you need?

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23 If a female fish is 2 1/2 inches long and the male is 2/3 as long as the female, how long is the male?

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24 A tape holds 6 hours of recording. John recorded 2 5/6 hours of a tv series. Does he have enough room to record a 3 1/4 hour show?

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25 The amount of silver in half-dollars was reduced from 9/10 to 2/5 in 1965. How much less is the silver content since the reduction?

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LCM / GCF Problems

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Charlotte goes to the movies with her friends once every 5 days. She goes out to dinner with her friends once every 6

• days. If she started this tradition with her

friends on June 1st, how many times will they do dinner and a movie on the same day by September 1st? Answer: 3 times. Students can reason out that each month has approximately 30 days.

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How many times will she do all 3 jobs in

• ne day?

Fold - every 4 days Deliver - every 3 days Collect - every 6 days Continues for 12 weeks The Macon Gazette is published every day rain or shine. Elizabeth helps her brother Joshua get the paper delivered. Elizabeth has a schedule that includes her folding the papers every 4th day, delivering the paper every 3rd day and collecting for the paper every 6th day. If she helps Joshua for 12 weeks, how many times will Elizabeth do all three jobs in

• ne day?

What do you know? What is the question to be answered?

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She will do all jobs on the same day 7 times. Do the jobs for 12 weeks (84 days) and count the days she does all 3 jobs (LCM) The Macon Gazette is published every day rain or shine. Elizabeth helps her brother Joshua get the paper delivered. Elizabeth has a schedule that includes her folding the papers every 4th day, delivering the paper every 3rd day and collecting for the paper every 6th day. If she helps Joshua for 12 weeks, how many times will Elizabeth do all three jobs in

• ne day?

What will you do to find the solution? Solve the problem and check here for the answer.

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How many pack of plates and forks should I buy? Forks come in packs of 18. Plates come in packs of 12. A package of forks contains 18 forks. A package of plates contains 12 plates. What is the fewest number of packages you would have to buy to have exactly the same number of forks and plates? What do you know? What is the question to be answered?

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Buy 2 packs of forks and 3 packs of plates. Keep buying plates and forks until the total is the same. (LCM) A package of forks contains 18 forks. A package of plates contains 12 plates. What is the fewest number of packages you would have to buy to have exactly the same number of forks and plates? What will you do to find the solution? Solve the problem and check here for the answer.

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In the concert there are 24 orchestra, 18 band and 36 chorus

• students. What is the maximum number of students per

row that can be in the picture if you want each row to contain students from only one program (i.e. all chorus)?

Pull Pull

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26 Pie crusts are sold in boxes of 3 and pie filling is sold in packages of 4 cans. What is the least number of pie crusts and filling that you should buy to have the same number of each?

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27 To make fruit punch you need equal amounts of apple, pineapple and grape juice. Apple juice is sold in 8 oz containers, pineapple in 12 oz and grape in 16 oz. How many containers of each juice should you buy?

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28 Jim is creating care packages to send overseas. He has 45 magazines and 36 books. Each package needs to have the same number of magazines as books. What is the greatest number of packages he can make?

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29 Sarah is passing out birthday treats. She has 14 cookies and 35 cupcakes. Does she have enough to divide equally among 7 guests?

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30 You are training for a triathlon. You run every 3 days, bike every 5 days and swim every 7 days. If you complete all three activities today, how many days from now will you next complete all three activities in the same day?

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Combination Problems

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How many days can Michael pack lunches before his lunches start to repeat? Michael doesn't like too many different foods for lunch. In fact, the only things that he will pack for lunch are a turkey, ham or tuna sandwich; a juice box or water bottle; potato chips, pop-corn or Doritos; and a whoopie pie or Tasty cake for dessert. If Michael does not want to pack a repeat lunch until after he has packed all the lunch possibilities, how many days will he be able to pack lunches before he starts to repeat combinations? turkey, ham or tuna sandwich juice or water potato chips, pop-corn or Doritos whoopie pie or Tasty cake What do you know? What is the question to be answered?

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3 x 2 x 3 x 2 = 36 combinations Michael doesn't like too many different foods for lunch. In fact, the only things that he will pack for lunch are a turkey, ham or tuna sandwich; a juice box or water bottle; potato chips, pop-corn or Doritos; and a whoopie pie or Tasty cake for dessert. If Michael does not want to pack a repeat lunch until after he has packed all the lunch possibilities, how many days will he be able to pack lunches before he starts to repeat combinations? Figure out how many combinations there are. What will you do to find the solution? Solve the problem and check here for the answer.

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How many different combinations of coins can total exactly $0.40? Answer: 31 different combinations. Create an

• rganized list.

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31 How many 3 topping sundaes can be made if you have 10 toppings to choose from?

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32 9 people are having dinner. If each person shakes the hand of each person, how many handshakes are there?

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33 There are 10 football players and 8 soccer players in the

• gym. How many different 2 player groups can be chosen

so there are no football players in the group?

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34 You have room on the wall to hang 4 posters but you have 6 to choose from. How many different combinations of posters are possible?

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35 Six people are running for Student Council President. In how many ways can the candidates be arranged to give their speeches?

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Proportion Problems

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Ten inches of snow is equivalent to

• ne inch of rain. If the forecast is for

2 1/2 inches on rain, how much snow would this be? Answer: 25 inches of snow or 2 feet 1 inch or 2 1/12 feet.

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The scale on a map is 2 cm = 5 inches. If the measurement between 2 cities on a map is 11 cm, how many miles is that? Answer: 27.5 miles or 27 1/2 miles

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In a photograph, the length of a sailing ship is 12 in, and the height of the mast is 5 in. The actual ship is 30 m

• long. What is the actual height of the ship's mast?

Answer: 12.5 m.

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In the pair of similar figures, what is the length of the missing side? Answer: 7.2 cm 5 cm 12 cm 3 cm

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36 If 2 pencils cost $1.50, how many pencils can you buy for $9.00?

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37 Joe ran 100 yards in 15 seconds. How long did it take him to run 3 yards?

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38 A car traveled 125 miles in 3 hours. How far did it travel in 5 hours?

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39 In a factory inspection, 14 out of 400 bulbs are found to be

• defective. How many defective bulbs can be expected in a

shipment of 1000?

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40 If Jennifer is 6 feet tall and casts a 4.3 foot shadow, how tall is a tree whose shadow is 16 feet?

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Geometry Problems

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A rectangular prism is made out of 1-centimeter cubes.

5 cm 2 cm 3 cm

What is the surface area of the rectangular prism? Show all work. What is the volume of the rectangular prism? Show all work.

surface area formula volume formula

Hint

Remember to use proper units when labeling your answer. If it helps, draw in the grid lines.

Answers

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Given 24 1-inch cubes, how can they be arranged to create a rectangular prism? Label each of the recangular prisms shown. Show 3 different examples (the cubes cannot be cut). l = w = h = l = w = h = l = w = h =

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A room has walls that are 12 ft long and 8 ft high. One wall contains a door that is 3 ft wide and 7 ft high. The room also has four windows that are 3 ft wide and 2 ft

• high. You want to paint the room - the 4

walls and the ceiling (the floor, windows and door are not to be painted). One can

• f paint covers 300 square feet and costs

$20. How much will it cost to paint the room?

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41 How many square centimeters of frosting are needed to frost a cake that is 35 cm x 65 cm x 2 cm?

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42 You want to tile your kitchen floor. The kitchen is 12 ft x 8 ft. How many 4 inch square tiles do you need to cover the floor?

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43 How much cookie dough can a cylindrical plastic container hold that is 4 inches tall with a 5 inch radius?

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44 A straw is 17 cm long with a diameter of 3 cm. How much material was needed to make the straw?

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45 One container of glass cleaner will clean 300 cm2 of glass. How many containers do you need to clean 5 windows measuring 100 cm x 250 cm? (You need to clean both sides of the glass!)

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Order of Operations Problems

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You can estimate the temperature in degrees Fahrenheit by counting the number of times a cricket chirps in 15 seconds and adding that number to 40.

• 1. What is the temperature if a cricket

is chirping 76 times per minute?

• 2. What is the temperature if a cricket

is not chirping at all? Answers: 1. About 59 degrees F.

• 2. It is impossible to tell, except that the

temperature must be 40 degrees or lower. Taken from grade 6 daily mathematics

• book. p.25, week 12, day 5.

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What is the expression that models this situation? Joy bought four snow globes at $7.00 each. She used a $2.00 coupon. After the coupon, the tax came to $1.96. Joy's father paid half

• f the final cost. Write an expression that

describes the situation and equals the total money paid by Joy. 4 snow globes at $7 each $2 coupon Tax after coupon is $1.96 Joy pays half the final cost What do you know? What is the question to be answered?

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(4 x 7 - 2 + 1.96) 2 Joy bought four snow globes at $7.00 each. She used a $2.00 coupon. After the coupon, the tax came to $1.96. Joy's father paid half

• f the final cost. Write an expression that

describes the situation and equals the total money paid by Joy. Use the correct order of operations. What will you do to find the solution? Solve the problem and check here for the answer.

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46 At the candy store, jelly beans are $3 per pound and chocolate is $7 per pound. How much will you pay for 3 pounds of jelly beans and 4 pounds of chocolate?

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47 Sarah has 2 disposable cameras with 24 pictures and 3 disposable cameras with 36 pictures. How many pictures can she take if she uses all the cameras?

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48 An adult ticket to the game is $5, a student ticket is $3 and a senior ticket is $4. How much does it cost for 3 adults, 4 seniors and 5 students to attend the game?

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49 There are 36 tables in a room. If 19 tables seat 8 people and the remaining tables seat 10 people, how many people can be seated in the room?

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50 Paint for a room costs $18 per gallon for the walls and $13 per gallon for the trim. If the room requires 3 gallons for the walls and 2 gallons for the trim, how much will it cost to paint?

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Integer Operations Problems

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A snail begins climbing from the bottom of a well that is 10 feet deep. Each day it climbs 3 feet and each night it slips down 2 feet. How many days does it take the snail to reach the top of the well? Answer: 8 days. The snail will not slide down after reaching the top of the well, that it why it will not take 10 days. Taken from grade 6 daily mathematics

• book. p.18, week 9, day 1.

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What is the difference between the elevation of the Dead Sea and Mt. Everest? The lowest elevation on Earth is on the shore of the Dead Sea, 1,310 feet below sea level. The highest elevation on Earth is Mt. Everest in the Himalayas at 29,028. What is the difference between the Dead Sea and Mt. Everest? The Dead Sea is 1,310 ft below sea level.

• Mt. Everest is 29,028 ft above sea level.

What do you know? What is the question to be answered?

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30,338 feet The lowest elevation on East is on the shore of the Dead Sea, 1,310 feet below sea level. The highest elevation on Earth is

• Mt. Everest in the Himalayas at 29,028.

What is the difference between the Dead Sea and Mt. Everest? Subtract the lower elevation from the higher elevation. What will you do to find the solution? Solve the problem and check here for the answer.

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An airplane is flying at 15,000 feet when it is asked to change course to 19,400 feet. What is the change in elevation of the airplane?

Pull Pull

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51 During the coldest day in winter, the windchill makes it feel 18 degrees colder. If the temperature is 5 degrees, what is the windchill?

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52 In the first four downs of a football game, the receiving team gained 6 yards, lost 11 yards, lost 4 yards and gained 13

• yards. What was their total number of yards gained or lost?

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53 A submarine is diving from 120 feet below the surface at a rate of 65 feet per minute. What is its depth after 5 minutes?

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54 You begin your hiking trip 85 feet above sea level and hike into a canyon 13 feet below sea level. What is the difference in altitudes?

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55 The highest temperature recorded in Death Valley is 134

• degrees. The lowest temperature recorded in Greenland is -

87 degrees. What is the temperature range?