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To calcuate using weighted averages

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To calcuate using weighted averages

by gmattesttaker2 » Tue Jan 21, 2014 1:47 am
Hello,

Can you please tell me how to solve the following using weighted averages:

At a party there are 60 men and 40 women. If 70 percent of the men and 80 percent of the women wear red t-shirts what percentage of all the people wear red t-shirts?


Thanks a lot,
Sri
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by theCodeToGMAT » Tue Jan 21, 2014 2:43 am
Red = 70% of 60M &&& 80% of 40W

To find: M

N1/N2 = (M2 - M) / (M - M1)
N1 = 70/100 * 60
N2 = 80/100 * 40

7*6/8*4 = (80 - M)/(M - 70)

21(M-70) = 16(80-M)
21M - 21*70 = 16*80 - 16M
37M = 16*80 + 21*70
37M = 1280 + 1470
M = 74 approx
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by GMATGuruNY » Tue Jan 21, 2014 5:33 am
gmattesttaker2 wrote: At a party there are 60 men and 40 women. If 70 percent of the men and 80 percent of the women wear red t-shirts what percentage of all the people wear red t-shirts?
Here, it seems easier simply to calculate the number of people who wear red t-shirts.
Since 70% of the 60 men wear red t-shirts, men who wear red t-shirts = .7(60) = 42.
Since 80% of the 40 women wear red t-shirts, women who wear red t-shirts = .8(40) = 32.
Of the 100 people, the percentage in red t-shirts = (total people in red-shirts)/(total people) = (42+32)/100 = 74%.
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