Jim is twice as old as Fred ...

I've added the answer choices....

II wrote:Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 4 times as old as Sam. How old is Jim now ?
A. 8
B. 12
C. 16
D. 20
E. 24

TODAY'S AGES
Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred.
Let x = Fred's age TODAY
So, 2x = Jim's age TODAY
And x - 2 = Sam's age TODAY

AGES FOUR YEARS AGO
Let's first determine Jim's age and Sam's age FOUR YEARS AGO
If 2x = Jim's age TODAY, then 2x - 4 = Jim's age FOUR YEARS AGO
If x - 2 = Sam's age TODAY, then x - 2 - 4 = Sam's age FOUR YEARS AGO

Four years ago Jim was 4 times as old as Sam.
In other words, the value of 2x - 4 is 4 times the value of x - 2 - 4
So, we can write: 2x - 4 = 4(x - 2 -4)
Simplify right side: 2x - 4 = 4(x - 6)
Expand right side: 2x - 4 = 4x - 24
Add 24 to both sides: 2x + 20 = 4x
Subtract 2x from both sides: 20 = 2x
Solve: x = 10

How old is Jim NOW?
2x = Jim's age TODAY
Since x = 10, we know that Jim's age = 2(10) = 20

Answer: D

Cheers,
Brent

II wrote:Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago Jim was 4 times as old as Sam. How old is Jim now ?

What is the best and quickest way to work this out ?

Thanks.
II

We can let J, S, and F = the current age of Jim, Fred, and Sam, respectively, and create the equations:

J = 2F

and

S = F - 2

S + 2 = F

and

J - 4 = 4(S - 4)

J - 4 = 4S - 16

J = 4S - 12

Since J = 2F we have:

2F = 4S - 12

F = 2S - 6

Since S + 2 = F, we have:

S + 2 = 2S - 6

8 = S

So J = 4 x 8 - 12 = 20.