Word Problems

[swerve]

\(2x + y\) yeas ago, Roberto was \(3x + y\) years old. How many years old was Roberto \(x\) years ago?

A. \(x\)
B. \(4x+2y\)
C. \(5x+2y\)
D. \(6x+2y\)
E. \(6x+y\)

The OA is B

Source: Magoosh

[Brent@GMATPrepNow]

\(2x + y\) yeas ago, Roberto was \(3x + y\) years old. How many years old was Roberto \(x\) years ago?

A. \(x\)
B. \(4x+2y\)
C. \(5x+2y\)
D. \(6x+2y\)
E. \(6x+y\)

The OA is B

Source: Magoosh

Let R = Roberto's PRESENT age.
So, R - x = Roberto's age X YEARS AGO (this is our goal!)
Also, R - (2x + y) = Roberto's age (2x + y) YEARS AGO

2x + y years ago, Roberto was 3x + y years old.
We can write: R - (2x + y) = 3x + y
Remove brackets: R - 2x - y = 3x + y
Add y to both sides to get: R - 2x = 3x + 2y
Add x to both sides to get: R - x = 4x + 2y

Answer: B

Cheers,
Brent

[Scott@TargetTestPrep]

\(2x + y\) yeas ago, Roberto was \(3x + y\) years old. How many years old was Roberto \(x\) years ago?

A. \(x\)
B. \(4x+2y\)
C. \(5x+2y\)
D. \(6x+2y\)
E. \(6x+y\)

The OA is B

Solution:

We can let r = Roberto’s age today and create the equation:

r - (2x + y) = 3x + y

r - 2x - y = 3x + y

r = 5x + 2y

We see that Roberto is currently (5x + 2y) years old. So x years ago, he was 5x + 2y - x = 4x + 2y years old.

Answer: B