SOLUTION: A women bought an number of items for $90. She realized that if she had bought 10 more for the same money she would have paid 12 less per item. How many items did she buy?

Question 1029405: A women bought an number of items for $90. She realized that if she had bought 10 more for the same money she would have paid 12 less per item. How many items did she buy?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x items * 90/x price per item=90
90/(x+10) is $12 less than 90/x
Therefore (90/(x+10))+12=90/x
multiply everything by (x)(x+10)
90x+12x^2+120x)=90x+900, clearing fractions.
12x^2+120x-900=0
divide everything by 12
x^2+10x-75=0
(x+15)(x-5)=0
x=5, only positive number
Paid $18 per item for 5 items
Had she bought 10 more, or 15 altogether, she would have paid $6 per item, which is $12 less.
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