SOLUTION: A grocer bought a number of items for 1,440 pesos.Later the price increased at 2 pesos per item and as a result he received 24 fewer items for the same amount.How many items were

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: A grocer bought a number of items for 1,440 pesos.Later the price increased at 2 pesos per item and as a result he received 24 fewer items for the same amount.How many items were       Log On


   

Question 977530: A grocer bought a number of items for 1,440 pesos.Later the price increased at 2 pesos 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?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x, first amount of items for 1440 pesos COST.
The price was 1440%2Fx PESOS per EACH.

Price Increased 2 pesos per item, bought 24 fewer items.
%281440%2Fx-2%29%28x-24%29=1440, the same cost.

%281440-2x%29%28x-24%29=1440x, multiplied both sides by x;
%28720-x%29%28x-24%29=720x, multiplied both sides by 1%2F2;
720x-x%5E2-24%2A720%2B24x=720x
-x%5E2-24%2A720%2B24x=0
x%5E2-24x%2B24%2A720=0

x=%2824%2B-+sqrt%2824%5E2%2B4%2A24%2A720%29%29%2F2, general solution formula

x=%2824%2B-+sqrt%2869696%29%29%2F2

x=%2824%2B-+264%29%2F2, but need the PLUS form.

x=%2824%2B264%29%2F2

highlight%28x=144%29--------this was how many items, the first time.