AlgebraMediumTwo unknowns from a count and a total
Algebra practice question
A pet shop sells hamsters for $15 each and mice for $6 each. On one day it sold 20 of these animals for a total of $174. How many hamsters did it sell that day?
Answer: 6
Let h be hamsters and m mice: h + m = 20 and 15h + 6m = 174. Substitute m = 20 − h: 15h + 120 − 6h = 174, so 9h = 54 and h = 6. Check: 6 hamsters ($90) and 14 mice ($84) total $174.
Common wrong answers
- If you answered 9
- 9 would come from 9h = 54 misdivided, or from (174 − 120) / 6 = 9 using the wrong per-animal difference. The difference in price is 15 − 6 = 9 per hamster, and 54 / 9 = 6.
- If you answered 14
- 14 is the number of MICE. The question asks for hamsters: 20 − 14 = 6.
- If you answered 11.6
- 11.6 is 174 / 15 — as if every animal were a hamster. The mice account for part of the total.
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