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?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> 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?       Log On


   

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) About Me  (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.