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This is fairly simple I'm sure, but I keep getting c. 30

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This is fairly simple I'm sure, but I keep getting c. 30 [#permalink] New post 05 Jul 2006, 19:55
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This is fairly simple I'm sure, but I keep getting c. 30 instead of a.15, the answer given by the OG (problem from OG 11, diagnostic test, #6 PS). My equation is 200= 60+3x=80-x

Thanks.
*************************************************
A marketing firm determined that, of 200 households surveyed, 80 used neither brand A nor brand B soap, 60 used only brand A soap, and for every household that used both brands of soap, 3 used only brand B soap. How many of the 200 households surveyed used both brands of soap?

a. 15
b. 20
c.30
d.40
e. 45


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 [#permalink] New post 05 Jul 2006, 22:33
Okay .......

80 use neither brand . Hence 120 people use either of the brands.

Let x be the number of people using both the brands.
Hence number of people using only brand B is 3x
Given: number of people using only brand A is 60

Hence

60 + x +3x = 120

4x = 60
x = 15
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 [#permalink] New post 06 Jul 2006, 18:38
Your venn diagram should give you the values:

#(A and B) = x
#(A only) = 60
#(B only) = 3x
#(Neither A nor B) = 80

So

x+60+3x+80 = 200
4x + 140 = 60
x = 15
  [#permalink] 06 Jul 2006, 18:38
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This is fairly simple I'm sure, but I keep getting c. 30

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