Sarah is four years younger than Joe. In five years, Joe will be twice Sarah's age now. How old are they now?
(SOLUTION 1)
Representation: Let x = Joe's age
x - 4 = Sarah's age
Present In five years
Sarah x - 4 x - 4 + 5 = x + 1
Joe x x + 5
Equation: In five years, Joe will be twice Sarah's age now, so, our equation would be: x + 5 = 2(x - 4)
Solution: x + 5 = 2(x - 4)
x + 5 = 2x - 8
Isolate the variable -- which means, group the variables on a certain side.
x - 2x = -8 - 5
- x = -13
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- x = -x
x = 13; x - 4 = 9
Answer: Joe is 13 years old while Sarah is 9 years old.
Check: x + 5 = 2(x - 4)
13 + 5 = 2(13 - 4)
18 = 26 - 8
18 = 18
(SOLUTION 2)
Representation: Let x = Sarah's age
x + 4 = Joe's age
Present In five years
Sarah x x + 5
Joe x + 4 x + 4 + 5 = x + 9
Equation: In five years, Joe will be twice Sarah's age now, so, the equation would be: x + 9 = 2x
Solution: x + 9 = 2x
9 = 2x - x
9 = x
x = 9; x + 4 = 13
Answer: Sarah is 9 years old while Joe is 13 years old.
Check: x + 9 = 2x
9 + 9 = 2(9)
18 = 18
