Jeff is 2 years younger than Carrie. 12 years agao, Carrie was twice as old as Jeff. How old is Jeff now?
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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Let's isolate J...
Let's add 10 to both sides...
Let's subtract 2J from both sides...
Let's check our work...
(16-12) ? 2(14-12)
4 ? 2(2)
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.
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
substituting in for c from equation above
distributing and combining like terms
subtracting j from each side and adding 24 to each side.
then c=16 and 12 years ago they were 2 and 4. Which checks out