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If Sara's age is exactly twice Bill's age, what is Sara's ag

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If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 18 Dec 2012, 07:43
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If Sara's age is exactly twice Bill's age, what is Sara's age?

(1) Four years ago, Sara's age was exactly 3 times Bill's age.
(2) Eight years from now, Sara's age will be exactly 1.5 times Bill's age.
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Re: If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 18 Dec 2012, 07:47
If Sara's age is exactly twice Bill's age, what is Sara's age?

Given: S = 2B.

(1) Four years ago, Sara's age was exactly 3 times Bill's age --> S - 4 = 3(B-4). We have two distinct linear equations (S - 4 = 3(B-4) and S = 2B) with two unknowns, thus we can solve for both. Sufficient.

(2) Eight years from now, Sara's age will be exactly 1.5 times Bill's age --> S + 8 =1.5(B + 8). The same here: we have two distinct linear equations with two unknowns, thus we can solve for both. Sufficient.

Answer: D.
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Re: If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 19 Mar 2013, 14:00
I solved this correctly via solving simultaneous equations ... but I could not understand the other approach the OG mentioned in the answer explanation : " another way to conclude that we can determine the value of s is to note that the pair of equations represents 2 non - parallel lines in the coordinate plane"
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Re: If Sara's age is exactly twice Bill's age, what is Sara's ag [#permalink] New post 06 Apr 2013, 04:48
TheNona wrote:
I solved this correctly via solving simultaneous equations ... but I could not understand the other approach the OG mentioned in the answer explanation : " another way to conclude that we can determine the value of s is to note that the pair of equations represents 2 non - parallel lines in the coordinate plane"


What they try to say is that the equations can be considered linear functions with different slopes. Therefore they will intersect at a certain point leading to one solution.
Re: If Sara's age is exactly twice Bill's age, what is Sara's ag   [#permalink] 06 Apr 2013, 04:48
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