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5 years ago a man was 7 times as old as his son. After 5 years the father will be 3 time as old as his son. Find their present age.

55 years ago a man was 77 times as old as his son. After 55 years the father will be 33 time as old as his son. Find their present age.

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Pythagorean Theorem and its converseright chevron icon

Full solution

Q. 55 years ago a man was 77 times as old as his son. After 55 years the father will be 33 time as old as his son. Find their present age.
  1. Set up equations: Step 11: Set up the equations based on the age relationships given in the problem.\newlineLet the current age of the father be FF and the son be SS.\newline55 years ago, the father was 77 times the age of his son: F−5=7(S−5)F - 5 = 7(S - 5)\newlineAfter 55 years, the father will be 33 times as old as his son: F+5=3(S+5)F + 5 = 3(S + 5)
  2. Simplify equations: Step 22: Simplify both equations.\newlineFrom the first equation: F−5=7S−35F - 5 = 7S - 35\newline⇒F=7S−30\Rightarrow F = 7S - 30\newlineFrom the second equation: F+5=3S+15F + 5 = 3S + 15\newline⇒F=3S+10\Rightarrow F = 3S + 10
  3. Solve for S: Step 33: Set the simplified expressions for F equal to each other to solve for S.\newline7S−30=3S+107S - 30 = 3S + 10\newline⇒7S−3S=10+30\Rightarrow 7S - 3S = 10 + 30\newline⇒4S=40\Rightarrow 4S = 40\newline⇒S=10\Rightarrow S = 10
  4. Find F: Step 44: Substitute the value of SS back into one of the original equations to find FF. Using F=7S−30F = 7S - 30: F=7(10)−30F = 7(10) - 30 ⇒F=70−30\Rightarrow F = 70 - 30 ⇒F=40\Rightarrow F = 40

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