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When Jenna spent 10 minutes on the elliptical and 20 minutes on circuit training, she burned 278 calories. When she spent 20 minutes on the elliptical and 30 minutes on circuit training, she burned 473 calories. Which system represents this, using e for calories per minute on the elliptical and c for calories per minute of circuit training?
A10e+20c=278 and 20e+30c=473
B10e+20c=473 and 20e+30c=278
C20e+10c=278 and 30e+20c=473
D10e+20c=278 and 30e+20c=473
Answer & Solution
Correct answer: A. 10e+20c=278 and 20e+30c=473
1. The first day's totals give the first equation: 10 minutes of elliptical time plus 20 minutes of circuit training equals 278 calories, written as 10e plus 20c equals 278.
2. The second day's totals give the second equation: 20 minutes of elliptical time plus 30 minutes of circuit training equals 473 calories, written as 20e plus 30c equals 473.
3. Swapping which day's total pairs with which equation, or swapping the minutes for e and c, would misrepresent the two days described.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.4 Solve Applications with Systems of Equations_
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