Question 763537
Let's say that there are {{{x}}}% medium shirts.
Since there are 1/3 as many small shirts as medium shirts,
there are {{{(1/3)x}}}% small shirts.
Since there are 1/2 as many large shirts as small shirts,
there are {{{(1/2)(1/3)x}}}% large shirts.
Since there are as many x-large shirts as large shirts,
there are {{{(1/2)(1/3)x}}}% x-large shirts.
The total is, off course {{{100}}}%, so
{{{x+(1/3)x+(1/2)(1/3)x+(1/2)(1/3)x=100}}}
Taking out {{{x}}} as a common factor, we get
{{{x(1+(1/3)+(1/2)(1/3)+(1/2)(1/3))=100}}}
Multiplying and adding those fractions, we get
{{{x(1+1/3+1/6+1/6)=100}}} --> {{{x(1+1/3+1/3)=100}}} --> {{{x(5/3)=100}}}
Multiplying both sides of the equation times {{{3/5}}}, we get the solution.
{{{x(5/3)=100}}} --> {{{x=100(3/5)}}} --> {{{x=100*3/5)}}} --> {{{highlight(x=60)}}}.
So 60% of the shirts are medium, 20% are small, 10% are large, and the remaining 10% are extra large.