Word problem

Question

Gary is x years old today.  Two years ago, his grandfather was 3 times older than Gary at that time.  The age difference of Gary and his grandfather then was 48 years.  What is the difference in their ages

Answer 1

Gary is X years old

Grandfather is Y years old

 

 

3(X-2) = Y-2

 

X-2 + 48 = Y-2 -->  X+48 = Y

 

 

3(x-2) = X+48 - 2

 

3x - 6 = X + 48 - 2

 

3x - 6 - x - 48 +2 = 0

 

2x - 52 = 0

 

2x = 52

 

x = 26

 

Gary is 26.

 

grandfather is 26 + 48 = 74

 

2 years ago, they were 24 and 72, 

 which is 48 years difference and

3 times as old.

 

The difference of their ages is 48 years.