SOLUTION: A student buys some pens for 400$. If the cost of each pens is 9$ less, he can buy 9 pens more from the same money. Find the number of pens

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Question 993318: A student buys some pens for 400$. If the cost of each pens is 9$ less, he can buy 9 pens more from the same money. Find the number of pens
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of pens
+400%2Fn+-+9+=+400%2F%28+n%2B9+%29+
Multiply both sides by +n%2A%28+n%2B9+%29+
+400%2A%28+n%2B9+%29+-+9%2An%2A%28+n%2B9+%29+=+400n+
+400n+%2B+3600+-+9n%5E2+-+81n+=+400n+
+9n%5E2+%2B+81n+-+3600+=+0+
+n%5E2+%2B+9n+-+400+=+0+
Use quadratic formula
+n+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+9+
+c+=+-400+
+n+=+%28+-9+%2B-+sqrt%28+9%5E2-4%2A1%2A%28-400%29+%29%29+%2F+%282%2A1%29+
+n+=+%28+-9+%2B-+sqrt%28+81+%2B+1600+%29%29+%2F+2+
+n+=+%28+-9+%2B-+sqrt%28+1681+%29%29+%2F+2+
+n+=+%28+-9+%2B+41+%29+%2F+2+
+n+=+32%2F2+
+n+=+16+
The student bought 16 pens
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check:
+400%2Fn+-+9+=+400%2F%28+n%2B9+%29+
+400%2F16+-+9+=+400%2F%28+16%2B9+%29+
+25+-+9+=+400%2F25+
+16+=+16+
OK