SOLUTION: A sorority buys a case of sweatshirts for $480 to sell at a mixer. The sorority needs to sell all but 16 of the sweatshirts at a profit of $5 per sweatshirt to regain the $480 inve

Question 1160413: A sorority buys a case of sweatshirts for $480 to sell at a mixer. The sorority needs to sell all but 16 of the sweatshirts at a profit of $5 per sweatshirt to regain the $480 investment. How many sweatshirts must be sold, and at what price, to do this?
_sweatshirts at $ _per sweatshirt
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
.


Let "n" be the number of sweatshirts .


From the condition, you have this equation to find n

     -  = 5  dollars.    (1)


Cancel the factor 5 in both sides

     -  = 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 =  =  = .


The only positive root is  n =   =  = 48.


ANSWER.  n = 48 shirts.


CHECK.  I will check equation (1):   -  =  -  = 15 - 10 = 5.

        ! Correct !

Solved.

RELATED QUESTIONS
A sorority set up a charity dinner to help raise money for a local children's support... (answered by richwmiller)

The class of 2011 is selling t-shirts and sweatshirts to raise money for the Junior Prom. (answered by rfer)

A sorority set up a charity to help raise money for a local children's support group.... (answered by FrankM)

The marching band holds a fund raiser each year in which they sell tshirts with the... (answered by ankor@dixie-net.com)

The Business Club buys 20 whole pizzas to sell at the game. Each pie has 8 slices. The... (answered by ikleyn)

Lester buys a TV for $200. At what price does he need to sell the TV for, if he wishes to (answered by stanbon)

Please help me solve this question: Jim bought 20 pants for $2,400 and marked them to... (answered by ankor@dixie-net.com)

Lori produces "Final Exam Care Packages" for resale by her sorority. She is currently... (answered by Mathtut)

Hi A grocer buys 20 cases of oranges at $15 a case. Each case has 10kg of oranges. If... (answered by jorel1380,MathTherapy)