SOLUTION: If 4 apples and 2 oranges equals $1 and 2 apples and 3 orange equals $0.70, how much does each apple and each orange cost? There are no quantity discounts.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If 4 apples and 2 oranges equals $1 and 2 apples and 3 orange equals $0.70, how much does each apple and each orange cost? There are no quantity discounts.      Log On


   

Question 152339: If 4 apples and 2 oranges equals $1 and 2 apples and 3 orange equals $0.70, how much does each apple and each orange cost? There are no quantity discounts.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Four apples + two Oranges = $1.00
4A%2B2O=1.00 -----------> eqn 1
Two apples + 3 Oranges = $0.70
2A%2B3O=0.70 ----------> eqn 2
in eqn 1, we get:
O=%281-4A%29%2F2 ----------> eqn 3
Substitute eqn 3 in eqn 2:
2A%2B3%281-4A%29%2F2=0.70 ------------> working eqn
2A%2B%283%2F2%29-3cross%284%292%2Fcross%282%29=0.70
2A%2B%283%2F2%29-6A=0.70
%283%2F2%29-0.70=6A-2A -----> cross%280.80%290.20%2Fcross%284%29=cross%284%29A%2Fcross%284%29
A=0.20 --------------> cost per apple
For Oranges, go back eqn 3:
O=%281-4%280.20%29%29%2F2
O=0.10 --------------> cost per orange
In doubt? go back eqn 2 this time:
2%280.20%29%2B3%280.10%29=0.70
0.40%2B0.30=0.70
0.70=0.70
Thank you,
Jojo