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Laney collected money for a Girl Scout camp. Each girl paid $75 and each adult paid $30, and the total collected was $765. The number of girls was three times the number of adults. How many girls and how many adults paid?
A3 girls and 9 adults
B12 girls and 4 adults
C9 girls and 3 adults
D6 girls and 2 adults
Answer & Solution
Correct answer: C. 9 girls and 3 adults
1. Let a stand for the number of adults, so the number of girls is 3a.
2. Each group contributes its price times its count: 75(3a) plus 30a equals 765.
3. Simplify the left side: 225a plus 30a equals 255a, so 255a equals 765.
4. Divide by 255: a equals 3 adults, and the girls number 3 times 3, which is 9.
5. Check: 9 girls paid $675 and 3 adults paid $90, and 675 plus 90 equals $765.
6. Swapping the groups to 3 girls and 9 adults breaks the three-times condition and only collects $495.
_Source: OpenStax Prealgebra (CC BY 4.0), Ch 9 "Math Models and Geometry", section 9.2 Solve Money Applications_
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