SOLUTION: A boy is 5 times as old as his sister two years ago the sum of the square of their ages was 170 find the present age of sister?

Question 1131713: A boy is 5 times as old as his sister two years ago the sum of the square of their ages was 170 find the present age of sister?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
b = 5s [the boy is 5 times as old as his sister]
Two years ago, the boy's age was b - 2, the sister's age was s - 2
(b-2)^2 + (s-2)^2 = 170
(5s-2)^2 + (s-2)^2 = 170
Solve for s:
25s^2 - 20s + 4 + s^2 - 4s + 4 = 170
26s^2 - 24s - 162 = 0
13s^2 - 12s - 81 = 0
Using the quadratic formula, we get s = 3, s = -2.077
Thus, the sister's age is 3, the brother's age is 15

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