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Two years ago Pete was three times as old as his cousin Claire. Two ye

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Bunuel
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Two years ago Pete was three times as old as his cousin Claire. Two ye [#permalink] New post   25 Apr 2019, 02:02
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Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be 2:1 ?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
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B
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Two years ago Pete was three times as old as his cousin Claire. Two ye [#permalink] New post   25 Apr 2019, 17:20
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1. Let's set up the two equations.

\(P-2 = 3(C-2)\)
\(P-4 = 4(C-4)\)



2. Now, we see that we can add 2 and 4 on both sides for the respective equations, we have 2 unique equations that give us P.
Set them equal to each other.

\(3C-6+2 = 4C-16+4\)
C = 8, then P must be 20 after plugging it back in.



3. Set up a new equation

\(20+x = 2(8-x)\)
x = 4

EDIT: I've expanded my explanation from the original post.
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Re: Two years ago Pete was three times as old as his cousin Claire. Two ye [#permalink] New post   29 Apr 2019, 10:13
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Bunuel wrote:
Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be 2:1 ?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 8



We can let P = Pete’s age now and C = Claire’s age now. We can create the equations:

P - 2 = 3(C - 2)

P - 2 = 3C - 6

P = 3C - 4

And

P - 4 = 4(C - 4)

P - 4 = 4C - 16

P = 4C - 12

Equating the equations, we have:

3C - 4 = 4C - 12

8 = C

So P = 3(8) - 4 = 20. Now let n be the number of years from now such that Pete will twice as old as Claire. We have:

20 + n = 2(8 + n)

20 + n = 16 + 2n

4 = n

Answer: B
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Re: Two years ago Pete was three times as old as his cousin Claire. Two ye [#permalink] New post   29 Apr 2019, 11:04
edlc313 wrote:
1. Let's set up the two equations.

\(P-2 = 3(C-2)\)
\(P-4 = 4(C-4)\)



2. Now, we see that we can add 2 and 4 on both sides for the respective equations, we have 2 unique equations that give us P.
Set them equal to each other.

\(3C-6+2 = 4C-16+4\)
C = 8, then P must be 20 after plugging it back in.



3. Set up a new equation

\(20+x = 2(8-x)\)
x = 4

EDIT: I've expanded my explanation from the original post.




\(20+x = 2(8-x)\)

It should by 20+x = 2(8+x)
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Re: Two years ago Pete was three times as old as his cousin Claire. Two ye [#permalink]
29 Apr 2019, 11:04
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