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Jeff is 2 years younger than Carrie. 12 years ago, Carrie was twice as old as Jeff. How old is Jeff now?

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3 Answers

Hi Jeff;
C-12=2(J-12)
C=J+2
 
Let's substitute...
(J+2)-12=2(J-12)
J-10=2J-24
Let's isolate J...
Let's add 10 to both sides...
10+J-10=2J-24+10
J=2J-14
Let's subtract 2J from both sides...
-2J+J=2J-14-2J
-J=-14
Jeff=14
Carrie=16
 
Let's check our work...
(16-12)   ?  2(14-12)
4  ?  2(2)
4=4
Mental math approach:
Since the differenc is 2 years old, 12 years ago, Carrie's age must be 4, and Jeff's age must be 2. So, Jeff's age is 12+2 = 14 years old, and Carrie's age is 12+4 = 16 years old.
 
Algebra approach:
Let J = Jeff's current age, and C = Carrie's current age.
J+2 = C ......(1)
2(J-12) = C-12 ......(2)
Plug in (1) into (2),
2(J-12) = J+2-12
Solve for J,
J = 14 years old
C = J+2 = 16 years old
J= C -2 represents jeff is 2 years younger than Carrie. 
Can also be written as C=J+2
 
12 years their ages could be written as j-12 and c-12 so Carrie was twice as old as Jeff can be written
c-12=2(j-12)
substituting in for c from equation above
j+2-12=2(j-12)
distributing and combining like terms
j-10=2j-24
subtracting j from each side and adding 24 to each side. 
14=j
then c=16 and 12 years ago they were 2 and 4. Which checks out
 

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