The sum of the ages of two brothers is 46. The younger brother is 10 more than 1/3 of the older brothers age. How old is the younger brother?

Question

Word problem

Answer 1

Let a and b be the respective ages for the brothers. Here's what we know:

a + b = 46

b = 1/3 a + 10

 

We have a value for b, so we can put that into our equation:

a + (1/3 a + 10) = 46

Simplify:

4/3 a + 10 = 46

Subtract 10 from both sides:

4/3 a = 36

 

Multiply both sides by 3/4

a = 36 * 3/4

a = 9 * 3/1

a = 27

Now to solve for b:

27 + b = 46

b = 19

 

Check:

19 = 1/3 * 27 + 10

19 = 9 + 10

19 = 19