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

Question

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

Answer 1

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

Answer 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.

 

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

Answer 3

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