SOLUTION: IF Taylor buys a dozen pieces of fruit for 99 cents. If an apple piece cost 3 cents more than on orange piece and she buys more apples than oranges, how many pieces of each type of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: IF Taylor buys a dozen pieces of fruit for 99 cents. If an apple piece cost 3 cents more than on orange piece and she buys more apples than oranges, how many pieces of each type of      Log On


   

Question 788735: IF Taylor buys a dozen pieces of fruit for 99 cents. If an apple piece cost 3 cents more than on orange piece and she buys more apples than oranges, how many pieces of each type of fruit did she buy.

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
A for number of Apples
N for number of Oranges (as in "naranjas").

A+N=12, total of 12 pieces of fruit.

Price for orange is y, units of CENTS. Price for apple is x.
x=3+y in units of CENTS.
ACCOUNTING for the cost, x*A+y*N=99;
%283%2By%29A%2BNy=99
3A%2BAy%2BNy=99
3A%2B%28A%2BN%29y=99
%28A%2BN%29y=99-3A
y=%2899-3A%29%2F%28A%2BN%29-----Use this to check the possible combinations for A and B.

We are given the restriction, A%3EN and we must have A and N as WHOLE numbers. We can check a few possible values for A and N, starting with A=7 & B=5 and continue checking, finding y for each pair of A and B, and reject any value of y that does not make sense.