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. 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 least 2 years old?
A.2
B.4
C.3✓ Correct
D.5
Explanation
Let parents' total age now = P, children's total = C, with n children. P = 6C; P−4 = 10(C−2n); P+12 = 3(C+6n). From first two: 6C−4 = 10C−20n ⟹ 20n−4 = 4C ⟹ C = 5n−1. From first and third: 6C+12 = 3C+18n ⟹ 3C = 18n−12 ⟹ C = 6n−4. So 5n−1 = 6n−4, n = 3.
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