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

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

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New post 17 Oct 2018, 02:51
1
1
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:29) correct 26% (01:11) wrong based on 58 sessions

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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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New post 17 Oct 2018, 06:11
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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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New post 17 Oct 2018, 06:22
1
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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New post 17 Oct 2018, 06:25
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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

Answer: B

Cheers,
Brent
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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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New post 17 Oct 2018, 13:35
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 .

The best answer is B.
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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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New post 18 Oct 2018, 18:18
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.

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