The sum of the ages of husband and wife at present is 60. Four years ago the…

Concept: When a problem gives the ratio of two people's ages at an earlier point in time along with their present-day total, represent the earlier ages using one common multiplier for the ratio (say 7x and 6x for a 7 : 6 ratio), then add the same fixed number of years to each to reach the present. The present-day total then gives a single linear equation in that multiplier.

Application:

1. Let the husband's age 4 years ago be 7x and the wife's age 4 years ago be 6x, since the ratio of their ages then was 7 : 6.

2. Their present ages are therefore 7x + 4 and 6x + 4.

3. The sum of their present ages is given as 60, so (7x + 4) + (6x + 4) = 60, i.e., 13x + 8 = 60.

4. Solving, 13x = 52, so x = 4.

5. The husband's present age = 7x + 4 = 7(4) + 4 = 32 years.

Cross-check: Check: the wife's present age = 6(4) + 4 = 28, and 32 + 28 = 60, matching the given total. Four years ago their ages were 28 and 24, and 28 : 24 reduces to 7 : 6, matching the given ratio — confirming the husband's present age is 32 years.