Slide 51 / 130 28 Solve the proportion using equivalent ratios x 4 60 12
Slide 52 / 130 29 Solve the proportion using equivalent ratios 3 21 x 28
Slide 53 / 130 In a proportion, the cross products are equal. 5 30 2 12 5 12 2 30 60 60
Slide 54 / 130 Proportions can also be solved using cross products. 4 12 Cross multiply 5 x 4x = 5 12 4x = 60 Solve for x x = 15 Example 2 7 x Cross multiply 8 48 8x = 7 48 8x = 336 Solve for x x = 42
Slide 55 / 130 30 Use cross products to solve the proportion 9 = x 51 17
Slide 56 / 130 Use cross products to solve the proportion 31 x = 56 12 96
Slide 57 / 130 Use cross products to solve the proportion 32 45 = _x 18 6
Slide 58 / 130 Use cross products to solve the proportion 33 2 = _x 15 60
Slide 59 / 130 34 Use cross products to solve the proportion 7 = _3 x 21
Slide 60 / 130 Application problems Return to Table of Contents
Slide 61 / 130 Chocolates at the candy store cost $5.99 per dozen. How much does one candy cost? Round your answer to the nearest cent. Solution: $5.99 1 dozen (Use equivalent rates) 1 dozen 12 $5.99 12 $0.50 per candy
Slide 62 / 130 Example 2: There are 3 books per student. There are 570 students. How many books are there? Set up the proportion: Books Students 3 Where does the 570 go? 1 3 x 1 570 1x 3 570 x 1,710 books
Slide 63 / 130 Example 3: The ratio of boys to girls is 4 to 5. There are 125 people on a team. How many are girls? Set up the proportion: Girls People How did we determine this ratio? 5 Where does the 125 go? = 9 5 x = 9 125 9x 5 125 = 9x = 625 x = 69.44 70 girls
Slide 64 / 130 35 Cereal costs $3.99 for a one pound box. What is the price per ounce? Round your answer to the nearest penny.
Slide 65 / 130 Which is the better buy? 36 Brand A: $2.19 for 12 ounces Brand B: $2.49 for 16 ounces Brand A A Brand B B
Slide 66 / 130 37 There are 4 girls for every 10 boys at the party. There are 56 girls at the party. How many boys are there?
Slide 67 / 130 38 The farmer has cows and chickens. He owns 5 chickens for every cow. He has a total of 96 animals. How many cows does he own?
Slide 68 / 130 39 The auditorium can hold 1 person for every 5 square feet. It is 1210 square feet. How many people can the auditorium hold?
Slide 69 / 130 40 The recipe for one serving calls for 4 oz of beef and 2 oz of bread crumbs. 50 people will be attending the dinner. How many lbs. of bread crumbs should be purchased?
Slide 70 / 130 41 Mary received 4 votes for every vote that Jane received. 1250 people voted. How many votes did Jane receive?
Slide 71 / 130 42 To make the desired shade of pink paint, Brandy uses 3 oz. of red paint for each oz. of white paint. She needs one quart of pink paint. How many oz. of red paint will she need?
Slide 72 / 130 43 In a sample of 50 randomly selected students at a school, 38 students eat breakfast every morning. There are 652 students in the school. Using these results, predict the number of students that eat breakfast. A 76 B 123 C 247 D 496 Question from ADP Algebra I End-of-Course Practice Test
Slide 73 / 130 Sampling Return to Table of Contents
Slide 74 / 130 Your task is to count the number of whales in the ocean or the number of squirrels in a park. How could you do this? What problems might you face?
Slide 75 / 130 How would you estimate the size of a crowd? What methods would you use? Could you use the same methods to estimate the number of wolves on a mountain?
Slide 76 / 130 One way to estimate the number of wolves on a mountain is to use the CAPTURE - RECAPTURE METHOD.
Slide 77 / 130 Suppose this represents all the wolves on the mountain.
Slide 78 / 130 Wildlife biologists first find some wolves and tag them.
Slide 79 / 130 Then they release them back onto the mountain.
Slide 80 / 130 They wait until all the wolves have mixed together. Then they find a second group of wolves and count how many are tagged.
Slide 81 / 130 Biologists use a proportion to estimate the total number of wolves on the mountain: = tagged wolves on mountain tagged wolves in second group total wolves on mountain total wolves in second group For accuracy, they will often conduct more than one recapture. 8 2 = w 9 2w = 72 w = 36 There are 36 wolves on the mountain
Slide 82 / 130 Try This: Biologists are trying to determine how many fish are in the Rancocas Creek. They capture 27 fish, tag them and release them back into the Creek. 3 weeks later, they catch 45 fish. 7 of them are tagged. How many fish are in the creek? 27 7 = f 45 27(45) = 7f 1215 = 7f 173.57 = f There are 174 fish in the river
Slide 83 / 130 A whole group is called a POPULATION. A part of a group is called a SAMPLE. When biologists study a group of wolves, they are choosing a sample . The population is all the wolves on the mountain. Population Sample
Slide 84 / 130 Example: 860 out of 4,000 people surveyed watched Grey's Anatomy. How many people in the US watched if there are 93.1 million people? 860 x = 4000 93,100,000 860(93,100,000) = 4000x 80,066,000,000 = 4000x 20,016,500 = x 20,016,500 people watched
Slide 85 / 130 Try This: 315 out of 600 people surveyed voted for Candidate A. How many votes can Candidate A expect in a town with a population of 1500?
Slide 86 / 130 Margin of Error The results of sampling are estimates, which always contain some error. The margin of error estimates the interval that is most likely to include the exact result for the population. Margin of error is given as a percent in the problem. To find the interval using margin of error: · Find the percent of the population · Add/Subtract that amount from the answer to create an interval.
Slide 87 / 130 860 out of 4,000 people surveyed watched Grey's Anatomy. How many people in the US watched if there are 93.1 million people? Estimate an interval with a 2% margin of error. Margin of Error = 2% This means 2% of the population ! l l l l a a c c 2% of 93,100,000 e e R R (.02)(93,100,000) 1,862,000 So the interval is 20,016,500 + 1,862,000 18,154,500 to 21,818,500
Slide 88 / 130 Try This: 6 out of 150 tires need to be realigned. How many out of 12,000 are going to need to be realigned? Estimate an interval with a 3% margin of error. Estimate r o r r E f o n i g r a M
Slide 89 / 130 44 You are an inspector. You find 3 faulty bulbs out of 50. Estimate the number of faulty bulbs in a lot of 2,000.
Slide 90 / 130 45 You are an inspector. You find 3 faulty bulbs out of 50. Estimate the number of faulty bulbs in a lot of 2,000. Use a 2% margin of error. What is the amount you are going to + by?
Slide 91 / 130 46 You are an inspector. You find 3 faulty bulbs out of 50. Estimate the number of faulty bulbs in a lot of 2,000. Use a 2% margin of error. What is the lower number in your interval?
Slide 92 / 130 47 You are an inspector. You find 3 faulty bulbs out of 50. Estimate the number of faulty bulbs in a lot of 2,000. Use a 2% margin of error. What is the upper number in your interval?
Slide 93 / 130 48 You survey 83 people leaving a voting site. 15 of them voted for Candidate A. If 3,000 people live in town, how many votes should Candidate A expect?
Slide 94 / 130 49 You survey 83 people leaving a voting site. 15 of them voted for Candidate A. If 3,000 people live in town, how many votes should Candidate A expect? Find an interval using a 3% margin of error. What is the amount you are going to + by?
Slide 95 / 130 50 You survey 83 people leaving a voting site. 15 of them voted for Candidate A. If 3,000 people live in town, how many votes should Candidate A expect? Find an interval using a 3% margin of error. What is the lower number in your interval?
Slide 96 / 130 51 You survey 83 people leaving a voting site. 15 of them voted for Candidate A. If 3,000 people live in town, how many votes should Candidate A expect? Find an interval using a 3% margin of error. What is the upper number in your interval?
Slide 97 / 130 Scale Drawings Return to Table of Contents
Slide 98 / 130 Scale drawings are used to represent objects that are either too large or too small for a life size drawing to be useful. Examples: A life size drawing of an ant or an atom would be too small to be useful. A life size drawing of the state of New Jersey or the Solar System would be too large to be useful.
Slide 99 / 130 A scale is always provided with a scale drawing. The scale is the ratio: drawing real life (actual) When solving a problem involving scale drawings you should: · Write the scale as a ratio · Write the second ratio by putting the provided information in the correct location (drawing on top & real life on the bottom) · Solve the proportion
Slide 100 / 130 Example: This drawing has a scale of "1:10", so anything drawn with the size of "1" would have a size of "10" in the real world, so a measurement of 150mm on the drawing would be 1500mm on the real horse.
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