Problem 19: Find ratio of ages Two years ago, X was six times as old as his son and two...
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Problem 19: Find ratio of ages**
Two years ago, X was six times as old as his son and two years hence, twice his age will be equal to seven times that of his son.
What is the ratio of their present ages?
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Show answer & explanation
Setting up the linear equations X - 2 = 6(S - 2) and 2(X + 2) = 7(S + 2) yields son's age S = 6 and father's age X = 26. The ratio of their present ages is 26 : 6 = 13 : 3.
Step-by-step Derivation:
Step 1: Two years ago: X - 2 = 6(S - 2) => X = 6S - 10.
Step 2: Two years hence: 2(X + 2) = 7(S + 2) => 2X + 4 = 7S + 14 => 2X = 7S + 10.
Step 3: Substitute X: 2(6S - 10) = 7S + 10 => 12S - 20 = 7S + 10 => 5S = 30 => S = 6.
Step 4: Father's age X = 6(6) - 10 = 26.
Step 5: Ratio X : S = 26 : 6 = 13 : 3.