Question

Five years ago, Max was twice as old as Bert. A year from now, the sum of their ages would be 30. How old are they now? Show your solution.

Answer 1

Max is 17 years old and Bert is 11 years old

Explanation:

System of Equations

Let's call

x = current age of Max

y = current age of Bert

x - 5 = age of Max five years ago

y - 5 = age of Bert five years ago

x + 1 = age of Max one year from now

y + 1 = age of Bert one year from now

According to the conditions of the problem:

x - 5 = 2(y - 5) [1]

x + 1 + y + 1 = 30 [2]

Operating and simplifying [1]:

x - 5 = 2y - 10

x = 2y - 5 [3]

Operating and simplifying [2]:

x + y + 2 = 30

x + y = 28 [4]

Substituting [3] in [4]:

2y - 5 + y = 28

Simplifying:

3y - 5 = 28

3y = 33

y = 33/3

y = 11

From [3]:

x = 2*11 - 5

x = 22 - 5

x = 17

Max is 17 years old and Bert is 11 years old