SOLUTION: A grocer bought a number of items for $14.40. Later the price increased at 2 money. Centavos per item and as a result he received 24 fewer items for the same amount. how many items

Question 936642: A grocer bought a number of items for $14.40. Later the price increased at 2 money. Centavos per item and as a result he received 24 fewer items for the same amount. how many items were in his first purchase and what was the cost per item?
This is a word problem in a certain chapter in our book which deals all about Quadratic Equations. I hope you could help me out. Thanks.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A grocer bought a number of items for $14.40.
Later the price increased by 2 Centavos per item and as a result he received 24 fewer items for the same amount.
how many items were in his first purchase and what was the cost per item?
:
let x = original cost per item
then
= original no. of item he could by
and
= no. of items bought after the price increase
:
Original no. of items - cost increase items = 24
- = 24
multiply equation by x(x+.02)
x(x+.02)* - x(x+.02)* = 24x(x+.02)
cancel the denominators and you have
14.40(x+.02) - 14.40x = 24x(x+.02)
14.40x + .288 - 14.40x = 24x^2 + .48x
combine like terms on the right
0 = 24x^2 + .48x - .288
Use the quadratic formula here a=24, b=.48, c=-.288
I got a positive solution of x = .1 which is 10 centavos
:
Find the no. of items; 144 items originally
:
:
We can check this by finding the no of items when the cost is .12 (2 cents more)
= 120 items, which is 24 items less
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