Question

Dianne is 23 years older than her daughter Amy. In 5 years, the sum of their ages will be 91. How old are they now?Amy is ? years old, and Dianne is ? years old.

Answer 1

Currently

Let Amy's current age be x. Since Dianne is 23 years older than her daughter, then she is (x + 23) years old.

In 5 years

Amy's age will be (x + 5) years.

Dianne's age will be:

`x+23+5=(x+28)\text{ years}`

The sum of their ages in 5 years is 91. Therefore, we have:

`(x+5)+(x+28)=91`

Solving, we have:

`\begin{gathered} x+5+x+28=91 \\ 2x=91-5-28 \\ 2x=58 \\ x=(58)/(2) \\ x=29 \end{gathered}`

Amy is 29 years old. Therefore, Dianne will be:

`29+23=52\text{ years old}`

ANSWER:

Amy is 29 years old, and Dianne is 52 years old.