Question

bert is twice as old as jeff. John is 4 years younger than bert. The sum of their ages is 31. How old is bert?

Answer 1

x = Bert's age

y = Jeff's age

z = John's age


Bert is twice as old as jeff mean:

x = 2 y

This is the same:

y = x / 2

John is 4 years younger than Bert mean:

z = x - 4

The sum of their ages is 31 mean:

x + y + z = 31


Now:

x + y + z = 31

x + x / 2 + x - 4 = 31

2 x / 2 + x / 2 + 2 x / 2 - 4 = 31

5 x / 2 - 4 = 31

Add 4 to both sides

5 x / 2 - 4 + 4 = 31 + 4

5 x / 2 = 35

Mutiply both sides by 2

5 x = 2 ∙ 35

5 x = 70

Divide both sides by 5

x = 70 / 5

x = 14


y = x / 2

y = 14 / 2

y = 7


z = x - 4

z = 14 - 4

z = 10


x = Bert's age = 14

y = Jeff's age = 7

z = John's age = 10


Bert is 14 yrs old.

Answer 2

Jeff's age ---- x
Bert's age --- 2x
John's age --- 2x - 4

x + 2x + 2x-4 = 31
5x = 35
x = 7

so Bert is 14