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A marketing firm determined that, of 200 households surveyed
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22 Sep 2016, 12:04
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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 marketing firm determined that, of 200 households surveyed
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22 Sep 2016, 12:05
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GreenlightTestPrep wrote:
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
Here's a step-by-step approach using the Double Matrix method.
Here, we have a population of 200 households , and the two characteristics are: - using or not using Brand A soap - using or not using Brand B soap
So, we can set up our matrix as follows (where "~" represents "not"):
80 used neither Brand A nor Brand B soap We can add this to our diagram as follows:
60 used only Brand A soap We get...
At this point, we can see that the right-hand column adds to 140, which means 140 households do NOT use brand B soap.
Since there are 200 households altogether, we can conclude that 60 households DO use brand B soap.
For every household that used BOTH brands of soap... Let's let x = # of households that use BOTH brands....
...3 used only Brand B soap. So, 3x = # of households that use ONLY brand B soap
At this point, when we examine the left-hand column, we can see that x + 3x = 60 Simplify to get 4x = 60 Solve to get x = 15
How many of the 200 households surveyed used BOTH brands of soap? Since x = # of households that use BOTH brands of soap, the correct answer here is: A
Re: A marketing firm determined that, of 200 households surveyed
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03 Jun 2019, 07:47
This math is little confusing to me - for example, for every household that used both brands of soap, 3 used only Brand B soap. how come we find 3 households use ONLY brand B? I request for little more elucidation , if there is any. Regards
Re: A marketing firm determined that, of 200 households surveyed
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22 Aug 2019, 13:26
1
GreenlightTestPrep wrote:
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
Quick and dirty:
200 people must be accounted for.
so 200 = (number of people in all the categories)
we've got 80 that didn't use anything, 60 that only used A, x that used both, and 3x that used B.
so 200 = 80 + 60 + 4x
60 = 4x
x = 15.
(Helps to draw a Ven diagram as well. That's how I set up the problem and then then came up with the equation from there..)
~~~~~~ Looks like the x and 3x is the most confusing part. The ratio between both and just B is 1:3 (for every 1 that does both we have 3 that do B). "Multiply" the ratio by x so that it's general. x:3x
Re: A marketing firm determined that, of 200 households surveyed
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16 Jun 2021, 09:13
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