AlgebraMediumSystem for a purchase problem
Algebra practice question
Three cakes and two pies cost $19, and one cake and one pie cost $8. If c and p are the prices of a cake and a pie, which system represents this?
- A. 3c + 2p = 19 and c + p = 8Correct
- B. 3c + 2p = 8 and c + p = 19
- C. 2c + 3p = 19 and c + p = 8
- D. 3c + 2p = 19 and c − p = 8
Answer: A. 3c + 2p = 19 and c + p = 8
Three cakes and two pies make 19; one of each makes 8. (Solution: c = 3, p = 5.)
Why the other answers are wrong
- B. 3c + 2p = 8 and c + p = 19
- The totals are swapped.
- C. 2c + 3p = 19 and c + p = 8
- The counts are swapped.
- D. 3c + 2p = 19 and c − p = 8
- c − p = 8 turns a sum into a difference.
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