SOLUTION: A shop sells a total of 55 Shirts one day. They sell them in the ratio of 8:3, mens shirts to womens shirts. How many mens shirts do they sell?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A shop sells a total of 55 Shirts one day. They sell them in the ratio of 8:3, mens shirts to womens shirts. How many mens shirts do they sell?      Log On


   

Question 974391: A shop sells a total of 55 Shirts one day. They sell them in the ratio of 8:3, mens shirts to womens shirts.
How many mens shirts do they sell?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

m = # of mens shirts
w = # of womens shirts

"A shop sells a total of 55 Shirts one day" tells us that m%2Bw+=+55. Solve for w

m%2Bw+=+55

m%2Bw-m+=+55-m

w+=+55-m

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"They sell them in the ratio of 8:3, mens shirts to womens shirts" which allows us to form this proportion m%2Fw+=+8%2F3

m%2Fw+=+8%2F3

3m+=+8w Cross multiply

3m+=+8%2855+-+m%29 Plug in w+=+55-m. Now solve for m.

3m+=+8%2855%29+%2B+8%28-m%29 Distribute

3m+=+440+-+8m

3m%2B8m+=+440+-+8m%2B8m

11m+=+440

11m%2F11+=+440%2F11

m+=+40

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Question: How many mens shirts do they sell?
Answer: 40

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Extra Work: Use that value of m to find w.

w+=+55-m

w+=+55-40 Plug in m = 40

w+=+15

So 15 womens shirts were sold.
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