Question 1160413
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Let "n" be the number of sweatshirts .


From the condition, you have this equation to find n

    {{{480/(n-16)}}} - {{{480/n}}} = 5  dollars.    (1)


Cancel the factor 5 in both sides

    {{{96/(n-16)}}} - {{{96/n}}} = 1.


To solve the equation, multiply both sides by n*(n-16). You will get then

    96n - 96*(n-16) = n*(n-16)


Simplify and reduce to the standard form quadratic equation

    96n - 96n + 96*16 = n^2 - 16n

    n^2 - 16n - 1536 = 0

    n = {{{(16 +- sqrt(16^2 + 4*1536))/2}}} = {{{(16 +- sqrt(6400))/2}}} = {{{(16 +- 80)/2}}}.


The only positive root is  n =  {{{(16 + 80)/2}}} = {{{96/2}}} = 48.


<U>ANSWER</U>.  n = 48 shirts.


<U>CHECK</U>.  I will check equation (1):  {{{480/(48-16)}}} - {{{480/48}}} = {{{480/32}}} - {{{480/48}}} = 15 - 10 = 5.

        ! Correct !
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Solved.