Question

Ben is 20 years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was 3 times as old as Daniel.

Answer 1

Ben is 33 years old

Answer 2

Answers – Daniel is 13 years old; Ben is 33 years old

WORKINGS

Let Ben’s age be ‘x’
Let Daniel’s age be ‘y’

Given: Ben is 20 years older than Daniel
x = y + 20 ….. (Equation I)

Given: Three years ago, Ben was 3 times as old as Daniel.
x – 3 = 3(y – 3) ….. (Equation II)

Substitute ‘y + 20’ for x in Equation II
x – 3 = 3(y – 3)
(y + 20) – 3 = 3(y – 3)
y + 20 – 3 = 3y – 9
y + 17 = 3y – 9
3y – y = 17 + 9
2y = 26
y = 13
Daniel is 13 years old ….. (Answer I)

Substitute 13 for the value of ‘y’ in equation I
x = y +20
x = 13 + 20
x = 33
Ben is 33 years old ….. (Answer II)