# Sarah is four years ypunger than joe. in five years joe will be twice sarah's age now. how old are they now?

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2015-04-06T13:58:38+08:00

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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
---------------
- 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

A
﻿nswer: Sarah is 9 years old while Joe is 13 years old.
﻿
﻿C﻿heck: ﻿x + 9 = 2x
9 + 9 = 2(9)
18 = 18