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# Robert is 15 years older than his brother Stan. However, y years ago

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Math Expert
Joined: 02 Sep 2009
Posts: 55668
Robert is 15 years older than his brother Stan. However, y years ago  [#permalink]

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05 Mar 2018, 21:27
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Difficulty:

15% (low)

Question Stats:

97% (02:18) correct 3% (00:01) wrong based on 37 sessions

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Robert is 15 years older than his brother Stan. However, y years ago Robert was twice as old as Stan. If Stan is now b years old and b > y, find the value of b — y.

(A) 13

(B) 14

(C) 15

(D) 16

(E) 17

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Posts: 55668
Re: Robert is 15 years older than his brother Stan. However, y years ago  [#permalink]

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05 Mar 2018, 21:29
Bunuel wrote:
Robert is 15 years older than his brother Stan. However, y years ago Robert was twice as old as Stan. If Stan is now b years old and b > y, find the value of b — y.

(A) 13

(B) 14

(C) 15

(D) 16

(E) 17

Check other Age Problems in our Special Questions Directory.
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Re: Robert is 15 years older than his brother Stan. However, y years ago  [#permalink]

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05 Mar 2018, 23:58
1
Bunuel wrote:
Robert is 15 years older than his brother Stan. However, y years ago Robert was twice as old as Stan. If Stan is now b years old and b > y, find the value of b — y.

(A) 13

(B) 14

(C) 15

(D) 16

(E) 17

From the questions stem, we can write the following equations
y Years ago, R - y = 2(S - y) -> R - y = 2S - 2y -> 2S - R = y

R = b + 15(Stan's current age is b)

Substituting the value of R in the first equation, we get

2b - (b + 15) = y -> b - 15 = y -> b - y = 15(Option C)
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Re: Robert is 15 years older than his brother Stan. However, y years ago  [#permalink]

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06 Mar 2018, 02:33
Bunuel wrote:
Robert is 15 years older than his brother Stan. However, y years ago Robert was twice as old as Stan. If Stan is now b years old and b > y, find the value of b — y.

(A) 13

(B) 14

(C) 15

(D) 16

(E) 17

Currently

Stan = x years
Robert = x+15 years

y Years ago

Stan = (x-y) years
Robert = (x+15-y) years

Also, (x+15-y) = 2*(x-y)

i.e. x-y = 15

given that x = b

hence, b-y = 15

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Re: Robert is 15 years older than his brother Stan. However, y years ago  [#permalink]

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08 Mar 2018, 11:34
Bunuel wrote:
Robert is 15 years older than his brother Stan. However, y years ago Robert was twice as old as Stan. If Stan is now b years old and b > y, find the value of b — y.

(A) 13

(B) 14

(C) 15

(D) 16

(E) 17

We can let r = Robert’s age today and b = Stan’s age today and create the equations:

r = b + 15

We can express Robert’s age y years ago as (r - y) and Stan’s age y years ago as (b - y). We know that at that time (y years ago), Robert’s age was twice Stan’s age. Thus, we have:

r - y = 2(b - y)

r - y = 2b - 2y

r + y = 2b

Substituting b + 15 for r, we have:

b + 15 + y = 2b

15 + y = b

15 = b - y

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Re: Robert is 15 years older than his brother Stan. However, y years ago   [#permalink] 08 Mar 2018, 11:34
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