Please solve

Question

Bart’s age is one third of his mother’s age. Seven years ago his age was one fifth of hers. How old are both now?

Answer 1

Let b = Bart's age and m = his mother's.

 

b = m/3                       Bart is 1/3 of his mother's age

so 3b = m

 

b-7 = (m-7)/5              Seven years ago, Bart was one fifth of his mother's age

 

Substitute 3b in place of m is the second equation and solve for b:

b-7 = (m-7)/5

b-7 = (3b-7)/5           [Substituted 3b in place of m]

5(b-7) = 3b-7

5b - 35 = 3b-7

2b = 28

 

b = 14

 

Solve for m:

m = 3b

m = 3*14

 

m = 42

 

Check:

b-7 = (m-7)/5

14-7 = (42-7)/5

7 = 35/5

7 = 7

Check!