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How to solve this question

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How to solve this question

by 4neg » Thu Jan 29, 2009 8:53 am
In a certain department store, which has four sizes of a specific shirt, there are 1/3 as many small shirts as medium shirts, and 1/2 as many large shirts as small shirts. If there are as many x-large shirts as large shirts, what percent of the shirts in the store are medium?
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by DanaJ » Thu Jan 29, 2009 9:16 am
1/3*m = s
1/2*l = s = 1/3*m, so this means that l = 2/3*m
l = xl = 2/3*m.
s + m + l + xl = Total, so 1/3*m+m+2/3*m+2/3*m = T or 8/3*m = total. This means that m = 3/8*T = 0,375*t = 37,5%*T.
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by masuarezdl » Thu Jan 29, 2009 10:17 am
Wouldnt the second equation be "(1/2)S = L"?
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by r_walid » Thu Jan 29, 2009 10:33 am
Dana, I agree with your procedure except that I think L = 1/2S

this means that the total = S+M+L+X = 1/3M + M+ 2*L (since L=X)
so The total = 5/3M

The question asks about the percentage of M from the total, so it's M/T = 3/5 or 60%
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by DanaJ » Thu Jan 29, 2009 10:43 am
I don't really know what to say... Can you please provide OA?>
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by BuckeyeT » Thu Jan 29, 2009 11:13 am
First post, so please forgive me if I'm misreading, but r_walid's calculation looks correct.

Same calculation process. Solve all for m. Know s+m+l+xl=100%
Total 5/3m=100%, so 3/5*100=60%.
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by dimonya » Sun Feb 01, 2009 12:51 pm
In a certain department store, which has four sizes of a specific shirt, there are 1/3 as many small shirts as medium shirts, and 1/2 as many large shirts as small shirts. If there are as many x-large shirts as large shirts, what percent of the shirts in the store are medium?

Easiest way is to bring everything to common units and regress everythinh through them .. So we have ..

S,M,L,XL
S=M/3
M=M
L= 1/2S=1/2(M/3)= M/6
XL= M/6

So all shirts are S+M+L+XL =M/3+M+2(M/6)=5M/3

Percentage of M is just M/all shirts = M/(5M/3) = 3/5

The hardest part is the wording .. i.e is it S=M/3 or S=3M ..
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by chiller » Mon Feb 02, 2009 4:49 am
For this question, I used the "plug in" method.

Knowns:
S = 1/3M
S= 1/2L
XL=L

Question:
M=?

Since I saw 1/3 and 1/2 in the fractions, I decided to pick a number to start out with that is divisible by both. I chose 60.

Let's say there are L=60.

From that,

XL=60
L=60
S=1/2L=1/2(60)=30

From the small, we also know that S=1/3M, therefore:

30 = 1/3M
M = 90.

The total of all the shirts together = 240.
So, the question is, what percentage of 240 is 90?

90/x = 240/100

Hence,
x=37.5%

Hope this helps.
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Resolve

by nattatob » Mon Feb 02, 2009 8:26 am
There are four sizes in that department; S, M, L and XL .

(1/3)(M) = S
(1/2)(S) = L
XL = L

S +M+ L + XL
(1/3)(M)+M+(1/2)(1/3)(M)+(1/2)(1/3)(M)

= M/3+3M/3+M/6+M/6
= 10M/6 = Total

M/Total = 6/10 = 60%
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by coffee5251 » Mon Feb 02, 2009 10:47 am
I also go 60%. What is the OA?
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Re: Resolve

by gabriel » Tue Feb 03, 2009 6:55 pm
nattatob wrote:There are four sizes in that department; S, M, L and XL .

(1/3)(M) = S
(1/2)(S) = L
XL = L

S +M+ L + XL
(1/3)(M)+M+(1/2)(1/3)(M)+(1/2)(1/3)(M)

= M/3+3M/3+M/6+M/6
= 10M/6 = Total

M/Total = 6/10 = 60%


Lol cute kid, but is there a point behind posting the picture.
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Re: Resolve

by mrsmarthi » Tue Feb 03, 2009 8:08 pm
I can see some weird formula on the kid's dress. Probably might want to convey - "BORN MATHEMATICIAN".

Hey BTW, kid is really cute. Now coming back to the solution, my approach is slightly different.

Given M be the count of Medium shirts.

1/ 3 Small = Medium ==> Small = 3M
Medium = M
1/2 Large = Small ==> Large = 2 Small = 6M
XL = L ==> Xl = 6M

% of Medium shirts = M / (3M + M + 6M +6M) * 100 =
==> 1/16 * 100 = 6 1/4

And my ans is - 6 1/4.
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