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Multi-Step Problem Solving in Exercise and Calories Burned

This document provides examples of how to solve multi-step problems related to exercise routines and calorie consumption. In one case, a workout comprises running and swimming for a total of 50 minutes, with distinct calorie-burning rates for each activity. It highlights the application of the distributive property, combining like terms, and forming equations. An example demonstrates finding the calories burned after specific running times, while guided practice challenges the reader to simplify expressions and apply learned methods to new situations like adjusting workout durations.

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Multi-Step Problem Solving in Exercise and Calories Burned

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  1. n +3 n + 30 5n + 3 5n + 30 C A B D ANSWER The correct answer is B. A B C D EXAMPLE 4 Standardized Test Practice Simplify the expression4(n + 9) – 3(2 + n). 4(n + 9) – 3(2 + n) = 4n + 36 – 6 – 3n Distributive property =n + 30 Combine like terms.

  2. EXAMPLE 5 Solve a multi-step problem EXERCISING Your daily workout plan involves a total of 50 minutes of running and swimming. You burn 15 calories per minute when running and 9 calories per minute when swimming. Let rbe the number of minutes that you run. Find the number of calories you burn if you run for 20 minutes. SOLUTION The workout lasts 50 minutes, and your running time is rminutes. So, your swimming time is (50 – r) minutes.

  3. Amount burned (calories) Swimming time(minutes) Running time (minutes) Burning rate when swimming (calories/minute) Burning rate when running (calories/minute) = + • • C= 5 r +9(50– r) EXAMPLE 5 Solve a multi-step problem STEP1 Write a verbal model. Then write an equation. C = Write equation. 15r + 9(50 – r) =15r + 450–9r Distributive property = 6r + 450 Combine like terms.

  4. ANSWER You burn 570 calories in your 50 minute workout if you run for 20 minutes and swim for 30 minutes. EXAMPLE 5 Solve a multi-step problem STEP2 Find the value of Cwhen r = 20. C = 6r+ 450 Write equation. = 6(20)+450 = 570 Substitute 20 for r. Then simplify.

  5. ANSWER You burn 525 calories in your 45 minute workout if you run for 20 minutes. You burn 585 calories in your 45 minute workout if you run for 30 minutes. for Examples 4 and 5 GUIDED PRACTICE 6. Simplify the expression5(6+ n) – 2(n – 2) =34 + 3n. 7. WHAT IF? In Example 5, suppose your workout lasts 45 minutes. How many calories do you burn if you run for 20 minutes?30 minutes?

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