Multiple choice

The sum of the ages of husband and wife at present is 56. Ten years ago, the product of their ages was 320. What is the age of the husband and the wife?

  1. 28, 28

  2. 32, 24

  3. 30, 26

  4. 29, 27
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let H and W be ages. H+W=56. 10 years ago: (H-10)(W-10)=320. (H-10)(56-H-10)=320. (H-10)(46-H)=320. 46H - H^2 - 460 + 10H = 320. H^2 - 56H + 780 = 0. Roots are 30 and 26.

AI explanation

Let the husband's present age be H and the wife's present age be W, so H + W = 56. Ten years ago, the product of their ages was 320, giving the equation (H - 10)(W - 10) = 320, which expands to HW - 10H - 10W + 100 = 320. Substituting W = 56 - H gives a quadratic equation of H^2 - 56H + 540 = 0, which factors to (H - 30)(H - 26) = 0. Therefore, the age of the husband and the wife is 30 and 26.

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