BTGModeratorVI wrote: ↑

Sun Sep 27, 2020 7:02 am

In 8 years, Leonard will be twice as many years old as Mikala is now. If Leonard were twice as old as he was 2 years ago, and if Mikala were five times as old as she was 2 years ago, the sum of their ages would be 51. What will be the sum of their ages in 3 years?

A. 12
B. 14
C. 19
D. 22
E. 25

Answer: E
Source: Kaplan

Let M = Mikala's PRESENT age
Let L = Leonard's PRESENT age

In 8 years, Leonard will be twice as many years old as Mikala is now
In 8 years, Leonard's age will be L + 8
So we can write: L + 8 = 2M
Rearrange the terms to get the variables on one side: L - 2M = -8


If Leonard were twice as old as he was 2 years ago, and if Mikala were five times as old as she was 2 years ago, the sum of their ages would be 51.
2 years ago Leonard's age was L - 2
2 years ago Mikala's age was M - 2
We can write: 2(L - 2) + 5(M - 2) = 51
Expand: 2L - 4 + 5M - 10 = 51
Rearrange and simplify to get: 2L + 5M = 65


What will be the sum of their ages in 3 years?
We now have the following system of equations:
L - 2M = -8
2L + 5M = 65

Multiply both sides of the top equation by 2 to get:
2L - 4M = -16
2L + 5M = 65

Subtract the bottom equation from the top equation to get: -9M = -81
Solve: M = 9
Now that we know the value of M, we can take any of our equations and replace M with 9 to determine the value of L.
When we do this we get L = 10

So, Mikala's PRESENT age is 9 and Leonard's PRESENT age is 10
So, IN THREE YEARS, Mikala will be 12 and Leonard will be 13
So the sum of their ages = 12 + 13 = 25

Answer: E

Cheers,
Brent