Bob is 8 years older than Sue. 4 years ago, Bob was twice as old as Sue. What is the sum of their current ages?

Question

make sure to define your variable, write an equation, and solve the equation.

 

Answer 1

Let's say that x is Sue's age.

 

So Bob's age is x+8.

 

To get their ages four years ago, just subtract 4 from each. So Sue's age was x-4, and Bob's age was x+8-4 = x+4.

 

So at that time, Bob's age, x+4, was twice as much as Sue's age, x-4.  That can be written as an equation:

 

x+4 = 2(x-4)

 

To solve that, simplify:

x+4 = 2x-8

 

Then add 8 to both sides:

x+12 = 2x

 

Subtract x from both sides:

12 = x

 

So Sue's age is 12 and Bob's (he is 8 years older) is 20.  So the sum of their ages is 32.