Henry’s age is 10 years less than 4 times Paul’s age. If the sum of their ages is equal to 25 years, find the age of each boy.

18 yrs and

7 years

Step-by-step explanation:

Let Henry’s age be A and Paul’s age be B

Given Henry’s age A is 10 yrs less than 4 times Paul’s age B.

That’s

A =4 x B - 10

A = 4B - 10

The sum of their ages is equal to 25

That’s

A + B = 25

Therefore,we no now have to equations

1. A = 4B - 10

2. A + B = 25

Now put 4B - 10 in place of A in equation 2

We have

A + B = 25

4B - 10 + B = 25

This can also be written as

4B + B - 10 = 25

5B - 10 = 25

Add 10 to both sides

5B - 10 + 10 = 25 + 10

5B = 35

Divide both sides by 5

5B/5 = 35/5

B = 7

Paul’s age = 7 yrs

Recall A = 4B - 10

and B= 7

Therefore,

A = 4 x 7 - 10

A = 28 - 10

A = 18

Henry’s age = 18 yrs

Their ages are 18 yrs and 7 years