SOLUTION: 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

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 763537: 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?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say that there are x% medium shirts.
Since there are 1/3 as many small shirts as medium shirts,
there are %281%2F3%29x% small shirts.
Since there are 1/2 as many large shirts as small shirts,
there are %281%2F2%29%281%2F3%29x% large shirts.
Since there are as many x-large shirts as large shirts,
there are %281%2F2%29%281%2F3%29x% x-large shirts.
The total is, off course 100%, so
x%2B%281%2F3%29x%2B%281%2F2%29%281%2F3%29x%2B%281%2F2%29%281%2F3%29x=100
Taking out x as a common factor, we get
x%281%2B%281%2F3%29%2B%281%2F2%29%281%2F3%29%2B%281%2F2%29%281%2F3%29%29=100
Multiplying and adding those fractions, we get
x%281%2B1%2F3%2B1%2F6%2B1%2F6%29=100 --> x%281%2B1%2F3%2B1%2F3%29=100 --> x%285%2F3%29=100
Multiplying both sides of the equation times 3%2F5, we get the solution.
x%285%2F3%29=100 --> x=100%283%2F5%29 --> x=100%2A3%2F5%29 --> highlight%28x=60%29.
So 60% of the shirts are medium, 20% are small, 10% are large, and the remaining 10% are extra large.