Exactly 8 years ago, Jim's son was twice as old as Jim's

AAPL wrote:Magoosh

Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If Jim’s son is now 5 years older than his daughter, how old is Jim’s daughter now?

A. 5
B. 10
C. 13
D. 16
E. 18

We can PLUG IN THE ANSWERS, which represent the daughter's current age.
When the correct answer is plugged in, the nd the dau

B: 10, implying that the daughter's age 8 years ago = 10-8 = 2
Since the son 8 years ago was twice as old as the daughter, the son's age 8 years ago = 2*2 = 4, implying that the son's age now = 4+8 = 12.
(son's current age) - (daughter's current age) = 12-10 = 2.
In this case, the difference between the current ages is TOO SMALL.
Eliminate B.

D: 16, implying that the daughter's age 8 years ago = 16-8 = 8
Since the son 8 years ago was twice as old as the daughter, the son's age 8 years ago = 2*8 = 16, implying that the son's age now = 16+8 = 24.
(son's current age) - (daughter's current age) = 24-16 = 8.
In this case, the difference between the current ages is TOO GREAT.
Eliminate D.

Since B yields a difference that is TOO SMALL, while D yields a difference that is TOO GREAT, the correct answer must be BETWEEN B AND D.

The correct answer is C.

C: 13, implying that the daughter's age 8 years ago = 13-8 = 5
Since the son 8 years ago was twice as old as the daughter, the son's age 8 years ago = 2*5 = 10, implying that the son's age now = 10+8 = 18.
(son's current age) - (daughter's current age) = 18-13 = 5.
Success!

AAPL wrote:Magoosh

Exactly 8 years ago, Jim’s son was twice as old as Jim’s daughter. If Jim’s son is now 5 years older than his daughter, how old is Jim’s daughter now?

A. 5
B. 10
C. 13
D. 16
E. 18

We can let Jim’s son’s current age = s and Jim’s daughter’s current age = d. We can also state that 8 years ago, his son was (s - 8) years old and his daughter was (d - 8) years old. We can create the following equation:

s - 8 = 2(d - 8)

s - 8 = 2d - 16

s = 2d - 8

and

s = 5 + d

Thus:

2d - 8 = 5 + d

d = 13

Answer: C