SOLUTION: A merchants purchased a box of pocket books for 720 pesos. When the price was reduced by 6 pesos per pocketbook, the merchant was able to purchase 6 more pocketbooks than the origi

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A merchants purchased a box of pocket books for 720 pesos. When the price was reduced by 6 pesos per pocketbook, the merchant was able to purchase 6 more pocketbooks than the origi      Log On


   

Question 1052880: A merchants purchased a box of pocket books for 720 pesos. When the price was reduced by 6 pesos per pocketbook, the merchant was able to purchase 6 more pocketbooks than the original number for the same amount of money. Find the original number of pocketbooks bought and the price per pocketbooks.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the original number of pocketbooks
+720%2Fn+ = the original price/pocketbook
+720%2Fn+-+6+ = the original price/pocketbook
reduced by 6 pesos/pocketbook
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[ reduced cost/pocketbook ]x[ new number of pocketbooks ] = [ same price ]
+%28+720%2Fn+-+6+%29%2A%28+n+%2B+6+%29+=+720+
+720+-+6n+%2B+4320%2Fn+-+36+=+720+
+-6n+%2B+4320%2Fn+-+36+=+0+
Multiply both sides by +n+
+-6n%5E2+%2B+4320+-+36n+=+0+
+6n%5E2+%2B+36n+-+4320+=+0+
+n%5E2+%2B+6n+-+720+=+0+
Use quadratic formula
+n+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+6+
+c+=+-720+
+n+=+%28+-6+%2B-+sqrt%28+6%5E2+-+4%2A1%2A%28-720%29+%29%29%2F%282%2A1%29+
+n+=+%28+-6+%2B-+sqrt%28+36+%2B+2880+%29%29+%2F+2+
+n+=+%28+-6+%2B+sqrt%28+2916+%29%29+%2F+2+
+n+=+%28+-6+%2B+54+%29%2F2+
+n+=+48%2F2+
+n+=+24+
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The original number of pocketbooks
bought was 24
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+720%2Fn+=+720%2F24+
+720%2Fn+=+30+
The price/pocketbook was 30 pesos
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check answer:
+%28+720%2Fn+-+6+%29%2A%28+n+%2B+6+%29+=+720+
+%28+720%2F24+-+6+%29%2A%28+24+%2B+6+%29+=+720+
+%28+30+-+6+%29%2A30+=+720+
+24%2A30+=+720+
+720+=+720+
OK