Answer:
Bert is 11 years old and Max is 17 years old.
Explanation:
System of Equations
To solve the system of equations, we use two variables x and y. Let's make:
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, five years ago, Max was twice as old as Bert, thus:
x - 5 = 2(y - 5) [1]
It's also known a year from now, the sum of their ages would be 30:
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 = 11
y = 11
From [3]:
x = 2*11 - 5
x = 22 - 5 = 17
x = 17
Max is 17 years old and Bert is 11 years old