SOLUTION: A woman bought a number of items for $120. She realized if she had bought 24 more items for the same money, she would have paid 16 less per item. How many items did she buy?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A woman bought a number of items for $120. She realized if she had bought 24 more items for the same money, she would have paid 16 less per item. How many items did she buy?       Log On


   



Question 1029401: A woman bought a number of items for $120. She realized if she had bought 24 more items for the same money, she would have paid 16 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+ = number of items she bought
+120+%2F+n+-+16+=+120%2F%28+n+%2B+24+%29+
Multiply both sides by +n%2A%28+n+%2B+24+%29+
+120%2A%28+n+%2B+24+%29+-+16%2An%2A%28+n+%2B+24+%29+=+120n+
+120n+%2B+2880+-+16n%5E2+-+384n+=+120n+
+16n%5E2+%2B+384n+-+2880+=+0+
+n%5E2+%2B+24n+-+180+=+0+
I can complete the square
+n%5E2+%2B+24n+=+180+
+n%5E2+%2B+24n+%2B+%2824%2F2%29%5E2+=+180+%2B+%2824%2F2%29%5E2+
+n%5E2+%2B+24n+%2B+144+=+180+%2B+144+
+%28+n+%2B+12+%29%5E2+=+324+
+%28+n+%2B+12+%29%5E2+=+18%5E2+
+n+%2B+12+=+18+
+n+=+6+
She bought 6 items
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check:
+120+%2F+n+-+16+=+120%2F%28+n+%2B+24+%29+
+120+%2F+6+-+16+=+120%2F%28+6+%2B+24+%29+
+20+-+16+=+120%2F30+
+4+=+4+
OK