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# 2x + y years ago, Roberto was 3x + y years old. How many years old was

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
2x + y years ago, Roberto was 3x + y years old. How many years old was  [#permalink]

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17 Oct 2018, 01:51
1
1
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:27) correct 25% (01:08) wrong based on 51 sessions

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2x + y years 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

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Joined: 09 Jun 2018
Posts: 189
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was  [#permalink]

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17 Oct 2018, 05:11
1
Now, Roberto is (3x+y) + (2x + y) = 5x + 2y years old
x years ago, he was 5x+2y - x = 4x + 2y years old.

Hence Option B.

Now, another way is to plug in numbers, say x = 1, y = 1.

So, 2*1 + 1 = 3 years ago Roberto was 3*1 + 1 = 4 years old. So, now, Roberto is 4+3 = 7 years old, x = 1 year ago, he was 6 years old. Check options now.
A: 1, Incorrect
B: 6, Correct
C: 7, Incorrect
D: 8, Incorrect
E: 7, Incorrect

Hence Option B again!
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was  [#permalink]

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17 Oct 2018, 05:22
Bunuel wrote:
2x + y years 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

OA: B

Let current age be $$z$$

According to Question,
$$z-(2x+y)=3x+y$$
$$z=5x+2y$$.........(1)

Age of Roberto $$x$$ years ago$$= z-x=5x+2y-x=4x+2y$$
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was  [#permalink]

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17 Oct 2018, 05:25
Top Contributor
Bunuel wrote:
2x + y years 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

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

Cheers,
Brent
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Concentration: Accounting, Finance
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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was  [#permalink]

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17 Oct 2018, 12:35
Bunuel wrote:
2x + y years 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

After 2x + y :

3x + y + 2x + y = 5x + 2y.

Before x years ago;

5x + 2y - x = 4x + 2y .

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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was  [#permalink]

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18 Oct 2018, 17:18
Bunuel wrote:
2x + y years 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

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.

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Re: 2x + y years ago, Roberto was 3x + y years old. How many years old was   [#permalink] 18 Oct 2018, 17:18
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