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.

x = 34, and y = 10.

The age of the uncle is 34 years and

The age of the nephew is 10 years now.

Step-by-step explanation:

Let x and y represent the ages of the uncle and nephew now respectively.

Given that;

The sum of the ages of an uncle and nephew 2 years ago was 40

(x-2) + (y-2) = 40

x+y - 4 = 40

x+y = 40+4

x+y = 44 ... 1

In 2 years time from now the age of the uncle will be 3 times that of his nephew by then.

(x+2) = 3 (y+2)

x+2 = 3y+6

Collecting the like terms;

x-3y = 6-2

x-3y = 4 ... 2

Solving the simultaneous equation;

Subtracting equation 2 from 1

x+y - (x-3y) = 44-4

y+3y = 40

4y = 40

y = 40/4 = 10

y = 10

Substituting y = 10 into equation 1;

x + 10 = 44

x = 44-10

x = 34

The age of the uncle is 34 years and

The age of the nephew is 10 years now.