SOLUTION: Nadine paid $4800 to buy a certain number of t-shirts for the math club members. Eight shirts were slightly damaged, so the store owner gave her 8 extra shirts effectively decreas

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Question 712387: Nadine paid $4800 to buy a certain number of t-shirts for the math club members. Eight shirts were slightly damaged, so the store owner gave her 8 extra shirts effectively decreasing the cost per item by $20. How many shirts (including the 8 extra) did she buy?
I will appreciate if the step by step solution is posted.
Thank you,
Ariel Halili

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of shirts she bought
The cost per item is +4800%2Fn+
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The owner gave her +8+ shirts, so then
she had +n+%2B+8+ shirts
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+4800+%2F+%28+n%2B8+%29+=+4800%2Fn+-+20+
This says:
( cost/shirt with 8 shirts added ) = ( $20 less than original cost/shirt )
Multiply both sides by +n%2A%28+n%2B8+%29+
+4800n+=+4800%2A%28+n%2B8+%29+-+20n%2A%28+n+%2B+8+%29+
+4800n+=+4800n+%2B+38400+-+20n%5E2+-+160n+
+-20n%5E2+-+160n+%2B+38400+=+0+
Divide both sides by +20+
+-n%5E2+-+8n+%2B+1920+=+0+
Use quadratic formula
+n+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-1+
+b+=+-8+
+c+=+1920+

+n+=+%28+8+%2B-+sqrt%28+64+%2B+7680+%29%29+%2F+%28-2%29+
+n+=+%28+8+%2B-+sqrt%28+7744+%29%29+%2F+%28-2%29+
+n+=+%28+8+%2B+88+%29+%2F+%28-2%29+
+n+=+96%2F%28-2%29+
+n+=+-48+ ( discard this result- can't be negative )
+n+=+%28+8+-+88+%29+%2F+%28-2%29+
+n+=+%28+-80+%29+%2F+%28-2%29+
+n+=+40+
She bought 40 + 8 = 48 shirts
check:
+4800+%2F+%28+n%2B8+%29+=+4800%2Fn+-+20+
+4800+%2F+%28+40%2B8+%29+=+4800%2F40+-+20+
+4800+%2F+48+=+4800+%2F+40+-+20+
+100+=+120+-+20+
+100+=+100+
OK