college algebra word problem study guide

Question

A man is currently 26 years older than his son. Twelve years from the current time, the man will be twice as old as his son. What is the current age of the father 

Answer 1

Let x = current age of father and y = current age of son

 

Currently: x = y + 26

 

Future: x+12 = 2(y+12)

 

Solve this using a system of equations. I'll choose the substitution method by replacing "x" in the second equation with "y+26".

 

(y+26)+12 = 2(y+12)

y+38 = 2y+24

 

Solving for y, we get y = 14, meaning the son's current age is 14. 

 

x = 14 + 26

x = 40

 

The father's current age is 40.