Question

the sum of the ages of an uncle and nephew 2 years ago was 40.In 2 years time from now the age of the uncle will be 3 times that of his nephew by then.Find their ages now

Answer 1

Uncle is 34. Nephew is 10.

Explanation:

Let u equal the age of the uncle, and n equal the age of the nephew.

First, two years ago, the sum of their ages was 40. We can represent this by subtracting 2 from each variable. Thus:

`(u-2)+(n-2)=40`

`u+n-4=40`

`u+n=44`

Next, in two years time, the uncle will be three times as old as his nephew. We can represent this by adding 2. Thus:

`u+2=3(n+2)`

We now have a system of equations and can solve accordingly.

First, from the first equation, we can determine that:

`u=44-n`

We can substitute this into the second equation.

`(44-n)+2=3(n+2)`

`46-n=3n+6`

`40=4n`

`n=10`

Thus, the nephew's age is 10.

And the uncle's age is 44-10 or 34.