SOLUTION: A woman bought a number of items for $24. She realized that if she had bought 3 more items for the same money, she would have paid $4 less per item. How many items did she buy?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A woman bought a number of items for $24. She realized that if she had bought 3 more items for the same money, she would have paid $4 less per item. How many items did she buy?      Log On


   

Question 1077404: A woman bought a number of items for $24. She realized that if she had bought 3 more items for the same money, she would have paid $4 less per item. How many items did she buy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of items she bought
+24%2Fn+ = the cost she paid per item
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If she bought +n%2B3+ items for $24, the cost per item
would have been +24%2Fn+-+4+
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I can say:
+24%2F%28+n%2B3+%29+=+24%2Fn+-+4+
Multiply both sides by +n%2A%28+n%2B3+%29+
+24n+=+24%2A%28+n%2B3+%29+-+4%2An%2A%28+n%2B3+%29+
+24n+=+24n+%2B+72+-+4n%5E2+-+12n+
+4n%5E2+%2B+12n+-+72+=+0+
+n%5E2+%2B+3n+-+18+=+0+
+%28+n+%2B+6+%29%2A%28+n+-+3+%29+=+0+ ( by looking at it )
+n+=+3+ ( can't use the negative solution )
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She bough 3 items
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check:
3 items for $24 is $8 per item
If she bought 3 more, or 6 items for $24, the
cost per item is $4, and this is $4 less than
the $8 per item actually paid.
OK