Multiple choice

The ratio of present ages of father and son is 7 : 2. Five years ago, the product of their ages was 150. What is the present age of the father?

  1. 30 years

  2. 45 years

  3. 35 years

  4. 40 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let ages be 7x and 2x. Five years ago, ages were 7x-5 and 2x-5. (7x-5)(2x-5) = 150. 14x^2 - 35x - 10x + 25 = 150. 14x^2 - 45x - 125 = 0. Solving for x, (x-5)(14x+25) = 0, so x=5. Father's age = 7*5 = 35.

AI explanation

Let the present ages of the father and son be 7x and 2x respectively. Five years ago, their ages were 7x minus 5 and 2x minus 5, so the equation is (7x minus 5) times (2x minus 5) equals 150. Expanding this gives 14x squared minus 45x plus 25 equals 150, which simplifies to 14x squared minus 45x minus 125 equals 0. Factoring this quadratic equation results in (2x minus 5) times (7x plus 25) equals 0, yielding x equals 5. The father's present age is 7 times 5, which is 35 years.

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