ktrout2020 wrote:Brent is 18 years younger than Justin. If in 5 years Brent will be half as old as Justin, how old was Justin 5 years ago?
A. 8
B. 18
C. 21
D. 26
E. 31
Source: Veritas
Here's a solution that uses 1 variable:
Brent is 18 years younger than Justin.
Let J = Justin's PRESET AGE
So, J-18 = Brent's PRESENT age
In 5 years, both people will be 5 years older
So, J + 5 = Justin's AGE IN 5 YEARS
And (J-18) + 5 = Brent's AGE IN 5 YEARS
Simplify to get: J - 13 = Brent's AGE IN 5 YEARS
In 5 years Brent will be half as old as Justin.
In other words, IN 5 YEARS 5 years, (Brent's age) = (1/2)(Justin's age)
We can write: J - 13 = (1/2)(J + 5)
Multiply both sides by 2 to get: 2J - 26 = J + 5
Solve to get: J = 31
So, Justin's PRESENT age = 31
How old was Justin 5 years ago?
Justin's age 5 years ago = 31 - 5 = 26
Answer: D
Cheers,
Brent
