## 53. Two Sisters

The age difference between two sisters is 4 years. If the cube of the age of the first one minus the cube of the age of the second one equals 988, how old is each sister?
53. Let $x$ be the age of the older sister, and $y$ be the age of the younger sister. Then

$$
x=y+4
$$

and

$$
x^{3}-y^{3}=988
$$

or

$$
(x-y)\left(x^{2}+x y+y^{2}\right)=988
$$

188

From this, we easily obtain

$$
12 y^{2}+48 y+64=988
$$

Therefore,

$$
y=7, \quad \text { and } x=11
$$