five years from now, a fathers age will be three times his sons age, and 5 years ago, he was seven times as old as his son was. what are their present ages

Question

five years from now, a fathers age will be three times his sons age, and 5 years ago, he was seven times as old as his son was. what are their present ages

Answer 1

Because we have 2 variables to solve for, we need 2 equations. From the question we get:

 

Father's Age + 5 Years = 3 x (Son's Age + 5 Years)

 

Father's Age - 5 Years = 7 x (Son's Age - 5 Years)

 

Simplify both equations:

 

Father's Age + 5 Years = 3 x Son's Age + 15 Years

 

Father's Age - 5 Years = 7 x Son's Age - 35 Years

 

Put both equations in terms of the Father's Age to make them equal

 

Equation 1:

 

Subtract 5 Years from both sides

 

Father's Age = 3 x Son's Age + 10 Years

 

Equation 2:

 

Add 5 Years to both sides

 

Father's Age = 7 x Son's Age - 30 Years

 

Combine the equations to get:

 

3 x Son's Age + 10 Years = 7 x Son's Age - 30 Years

 

Add 30 Years to each side and subtract 3 x Son's Age from each side

 

40 Years = 4 x Son's Age

 

Divide both sides by 4

 

Son's Age = 10 Years

 

Sub in Son's Age to solve for Father's Age

 

Father's Age = 3 x (10 Years) + 10 Years = 40 Years

 

The father is 40 years old and his son is 10 years old.