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Proportions, Equivalent Ratios, and Problem Solving

Learn how to solve problems using proportions and equivalent ratios. Practice writing and solving proportions to find missing values. Find the constant of proportionality. Lesson includes examples in clothing, cooking, and more.

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Proportions, Equivalent Ratios, and Problem Solving

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  1. Use proportions to solve problems. • equivalent ratios • proportion • cross products • constant of proportionality Lesson 3 MI/Vocab

  2. Interactive Lab:Solving Problems Lesson 3 Key Concept 1

  3. shirts shirts time time Write and Solve a Proportion CLOTHINGMelvin can decorate 8 t-shirts in 3 hours. At this rate, write and solve a proportion to find the time it will take him to decorate 20 t-shirts. Write a proportion. Let t represent the time in hours. Lesson 3 Ex1

  4. Write and Solve a Proportion Write the proportion. Find the cross products. Multiply. Divide each side by 8. Simplify. Answer:It will take Melvin 7.5 hours to decorate 20 t-shirts. Lesson 3 Ex1

  5. CLOTHING Adrian can decorate 5 t-shirts in 2 hours. At this rate, write and solve a proportion to find the time it will take her to decorate 18 t-shirts. • A • B • C • D A. 6.5 hours B. 7 hours C. 7.2 hours D. 7.6 hours Lesson 3 CYP1

  6. cups of flour cups of flour total people served total people served COOKINGA recipe serves 10 people and calls for 3 cups of flour. If you want to make the recipe for 15 people, how many cups of flour should you use? Write a proportion. Let c represent the number of cups of flour needed to serve 15 people. Lesson 3 Ex2

  7. Find the cross products. Multiply. Divide each side by 10. Simplify. Answer: You will need 4.5 cups of flour to make the recipe for 15 people. Lesson 3 Ex2

  8. COOKINGA recipe serves 12 people and calls for 5 cups of sugar. If you want to make the recipe for 18 people, how many cups of sugar should you use? • A • B • C • D A. 6.5 cups B. 6.7 cups C. 7.2 cups D. 7.5 cups Lesson 3 CYP2

  9. Write and Use an Equation FOOD Haley bought 4 pounds of tomatoes for $11.96. Write an equation relating the cost to the number of pounds of tomatoes. How much would Haley pay for 6 pounds at this same rate? for 10 pounds? Find the constant of proportionality between cost and pounds. The cost is $2.99 per pound. Lesson 3 Ex3

  10. Write and Use an Equation The cost is $2.99 times the number of pounds. Words Let c represent the cost.Let p represent the number of pounds. Variable Equation c = 2.99 ● p Use this same equation to find the cost for 6 and 10 pounds of tomatoes sold at the same rate. Lesson 3 Ex3

  11. Write and Use an Equation Write the equation. Replace p with the number of pounds. Multiply. Answer:The cost for 6 pounds of tomatoes is $17.94 and for 10 pounds is $29.90. Lesson 3 Ex3

  12. FOOD Cameron bought 3 pounds of apples for $11.37. Write an equation relating the cost to the number of pounds of apples. How much would Cameron pay for 5 pounds at this same rate? • A • B • C • D A. $18.95 B. $19.20 C. $19.85 D. $20.15 Lesson 3 CYP3

  13. TEETH:For every 6 people who say they floss daily, there are 14 people who say they do not. Write and Solve a proportion to determine out of 50 people how many you would expect to say they do floss daily.

  14. ILLNESS:For every person who actually has the flu, there are 5 people who have the same symptoms but with only a cold. If a doctor sees 60 patients, write and solve a proportion to determine how many of these you would expect to only have a cold.

  15. PHOTOGRAPHY:It takes 3 minutes to print out 4 digital photos. Write an equation relating the number of photos, n, to the number of minutes, m. • At this rate, how long will it take to print 10 photos?

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