Problem Solving

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?

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.

Wouldnt the second equation be "(1/2)S = L"?

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%

I don't really know what to say... Can you please provide OA?>

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%.

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 ..

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.

I also go 60%. What is the OA?

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.

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.