The sum of a mother’s and daughter’s ages is (56) years. After (4) years, the mother’s age will be (3) times the daughter’s age. What is the daughter’s present age?

Correct answer: 12 years

Let the mother’s present age be \(x\) years and the daughter’s present age be \(y\) years. Then \(x+y=56\). The condition after 4 years gives \(x+4=3(y+4)\). Hence \(x=3y+8\). Substituting in the first equation, \(3y+8+y=56\), so \(4y=48\) and \(y=12\). Therefore, the daughter’s present age is 12 years. For example, 14 years does not satisfy the total-age condition. Exam tip: in age problems, add the stated number of years to both persons’ present ages.