Brent is 18 years younger than Justin. If in 5 years Brent w

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

Hi All,

We're told that Brent is 18 years younger than Justin and in 5 years, Brent will be half as old as Justin. We're asked how old was Justin was 5 YEARS AGO. This is an example of a 'System math' question that involves a 'time shift.' We can solve this with some standard Algebra as long as we properly handle the 'time shift' with the following equations:

B = Brent's age today
J = Justin's age today

B = J - 18
(B + 5) = (1/2)(J + 5)

Here, we have a 'system' (2 variable and 2 unique equations), so we can solve it. Since we're focused on the value of J, I'm going to 'substitute in' the value for B...

(J - 18 + 5) = (1/2)(J + 5)
(J - 13) = (1/2)(J + 5)
2J - 26 = J + 5
J = 31

The question asks how old Justin was 5 YEARS AGO. Since he's 31 today, he was 31 - 5 = 26 years old five years ago.

Final Answer: [spoiler=]D[/spoiler]

GMAT assassins aren't born, they're made,
Rich

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

We can let b = Brent’s current age and j = Justin’s current age.

Since Brent is 18 years younger than Justin:

b = j - 18

In 5 years, Brent will be (b + 5) years old and, Justin will be (j + 5) years old, and Brent will be half as old as Justin:

b + 5 = (1/2)(j + 5)

2b + 10 = j + 5

2b + 5 = j

We can substitute 2b + 5 for j in the first equation, and we have:

b = 2b + 5 - 18

b = 13

Thus, Justin is 18 + 13 = 31 years old, so he was 26 five years ago.

Answer: D