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Example 5.38 from Elementary Algebra, 5.4 Solve Applications with Systems of Equations
Solve Applications with Systems of Equations: example 5.38
Translate to a system of equations and then solve:
When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for 20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes on the elliptical trainer and 30 minutes circuit training she burned 473 calories. How many calories does she burn for each minute on the elliptical trainer? How many calories does she burn for each minute of circuit training?
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Step 1. Read the problem. Step 2. Identify what we are looking for. We are looking for the number of
calories burned each minute on the
elliptical trainer and each minute of
circuit training.Step 3. Name what we are looking for. Let number of calories burned per minute on the elliptical trainer.
number of calories burned per minute while circuit trainingStep 4. Translate into a system of equations. 10 minutes on the elliptical and circuit
training for 20 minutes, burned
278 calories20 minutes on the elliptical and
30 minutes of circuit training burned
473 caloriesThe system is: Step 5. Solve the system of equations. Multiply the first equation by −2 to get opposite coefficients of e. Simplify and add the equations.
Solve for c.Substitute c = 8.3 into one of the original equations to solve for e. Step 6. Check the answer in the problem. Check the math on your own. Step 7. Answer the question. Jenna burns 8.3 calories per minute
circuit training and 11.2 calories per
minute while on the elliptical trainer.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Translate to a system of equations and then solve:
Mark went to the gym and did 40 minutes of Bikram hot yoga and 10 minutes of jumping jacks. He burned 510 calories. The next time he went to the gym, he did 30 minutes of Bikram hot yoga and 20 minutes of jumping jacks burning 470 calories. How many calories were burned for each minute of yoga? How many calories were burned for each minute of jumping jacks?
How did it go?