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abc ps [#permalink] New post 23 Jan 2006, 08:09
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Question Stats:

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If a,b, and c are positive numbers such that
[a/(a+b)](10) + [b/(a+b)](20)= c and if a < b, which of the following could be the value of c?

A. 10
B. 12
C. 15
D. 18
E. 30
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 [#permalink] New post 23 Jan 2006, 09:15
here are my thoughts...

10[a/(a+b) + 2b/(a+b)] = c just factored out the 10

(a+2b) / (a+b) = c/10 divided both sides by 10... and added numerators b/c they have same denominator

think of it kind of like a ratio... (a + 2b) = c and (a+b) = 10

what are all the possibilities where a+b = 10 and a<b
(4,6)
(3,7)
(2,8)
(1,9)

plug these into a + 2b to find the value of c.. it is 18.

There may be an easier way with out plugging in, but this seems to work.
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 [#permalink] New post 23 Jan 2006, 11:03
andrewhh82 wrote:
here are my thoughts...

10[a/(a+b) + 2b/(a+b)] = c just factored out the 10

(a+2b) / (a+b) = c/10 divided both sides by 10... and added numerators b/c they have same denominator

think of it kind of like a ratio... (a + 2b) = c and (a+b) = 10

what are all the possibilities where a+b = 10 and a<b
(4,6)
(3,7)
(2,8)
(1,9)

plug these into a + 2b to find the value of c.. it is 18.

There may be an easier way with out plugging in, but this seems to work.
:cool agree good job
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 [#permalink] New post 23 Jan 2006, 12:19
simple and easy good gooing :)
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Director
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 [#permalink] New post 24 Jan 2006, 12:12
great work andrewhh82

the oa is 18
  [#permalink] 24 Jan 2006, 12:12
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