Advanced MathMediumRational equation from a sharing context
Advanced Math practice question
A prize of $60 is shared equally among n winners. If there had been 2 more winners, each share would have been $5 less. How many winners were there? (Use 60/n − 60/(n + 2) = 5.)
Answer: 4
Multiply by n(n + 2): 60(n + 2) − 60n = 5n(n + 2), so 120 = 5n² + 10n, n² + 2n − 24 = (n + 6)(n − 4) = 0, n = 4. (Check: 15 − 10 = 5 ✓.)
Common wrong answers
- If you answered 6
- 6 is the size of the rejected negative root, −6.
- If you answered 10
- 10 is the share with 2 more winners.
- If you answered 15
- 15 is each winner's share in dollars, not the number of winners.
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