SOLUTION: A storeowner buys a quantity of tennis ball for $600. If they had each cost $0.25 less, she would have had 10 more for the same money. How much did she pay for each ball? Thanks

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Question 536713: A storeowner buys a quantity of tennis ball for $600. If they had each cost $0.25 less, she would have had 10 more for the same money. How much did she pay for each ball?
Thanks:)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of tennis balls she bought
Her cost/ball is +600%2Fn+
The cost/ball minus 25 cents is +600%2Fn+-+.25+
given:
( cost/ball ) x ( number of balls ) = cost
+%28+600%2Fn+-+.25+%29%2A%28+n+%2B+10+%29+=+600+
-----------------------------
+600+-+.25n+%2B+6000%2Fn+-+2.5+=+600+
Subtract 600 from both sides
+-.25n+%2B+6000%2Fn+-+2.5+=+0+
+-.25n+%2B+6000%2Fn+=+2.5+
Multiply both sides by n
+-.25n%5E2+%2B+6000+=+2.5n+
+-.25n%5E2+-+2.5n+%2B+6000+=+0+
Multiply both sides by +4+
+-n%5E2+-10n+%2B+24000+=+0+
Use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-1+
+b+=+-10+
+c+=+24000+

+n+=+%28+10+%2B-+sqrt%28++100+%2B+96000+%29%29%2F%28-2%29+
+n+=+%28+10+-+310%29%2F%28-2%29+ ( use the (-) square root )
+n+=+-300%2F-2+
+n+=+150+
She paid $600 for 150 balls, so she paid
+600+%2F+150+=+4+
$4 for each ball
check answer:
+%28+600%2Fn+-+.25+%29%2A%28+n+%2B+10+%29+=+600+
+%28+600%2F150+-+.25+%29%2A%28+150+%2B+10+%29+=+600+
+%28+4+-+.25+%29%2A160+=+600+
+3.75%2A160+=+600+
+600+=+600+
OK