The combined age of a man and his wife is 6 times the combined age of their children. Two years ago their combined age was 10 times the combined age of their children; and six years later their combined age will be 3 times the combined age of their children. How many children do they have if each child is at <strong>LEAST</strong> 2 years old?
- A. 2
- B. 3 ✓
- C. 4
- D. 5
Correct Answer: B. 3
Explanation
Let P be parents' combined age, C be children's combined age, and n be the number of children. P = 6C. Two years ago: P-4 = 10(C-2n). Six years later: P+12 = 3(C+6n). Substitute P=6C: 6C-4 = 10C-20n \implies 4C = 20n-4 \implies C = 5n-1. Also 6C+12 = 3C+18n \implies 3C = 18n-12 \implies C = 6n-4. Equating C: 5n-1 = 6n-4 \implies n=3.
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