SOLUTION: four oranges and five apples cost $3.56.three oranges and four apples cost $2.76.find the cost of an orange and the cost of an apple.

Algebra ->  Systems-of-equations -> SOLUTION: four oranges and five apples cost $3.56.three oranges and four apples cost $2.76.find the cost of an orange and the cost of an apple.       Log On


   

Question 118926: four oranges and five apples cost $3.56.three oranges and four apples cost $2.76.find the cost of an orange and the cost of an apple.
Found 2 solutions by checkley71, MathLover1:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
4O+5A=3.56
3O+4A=2.76
NOW MULTIPLY THE FIRST EQUATION BY 3 & THE SECOND EQUATION BY -4 & ADD:
12O+15A=10.68
-12O-16A=-11.04
------------------------
-A=-.36
A=.36 WHICH IS THE PRICE OF ONE APPLE.
4O+5*.36=3.56
4O+1.80=3.56
4O=3.56-1.80
4O=1.76
O=1.76/4
A=.44 FOR 1 ORANGE.
PROOF:
3*.44+4*.36=2.76
1.32+1.44=2.76
2.76=2.76

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if four+oranges=x and five+apples=y cost $3.56, then we have:
4x+%2B+5y+=3.56
if three+oranges=x and four+apples=y cost $2.76, then we have:
3x+%2B+4y+=2.76

solve the system:
I will solve it by addition.
4x+%2B+5y+=3.56..........multiply both sides by 3
3x+%2B+4y+=2.76..........multiply both sides by -4
-------------------
cross%2812x%29+%2B+15y+=10.68....
+cross%28-12x%29+-+16y+=+-+11.04....
-----------------------------------
15y+-+16y+=+10.68+-+11.04
-y+=+-+0.36.........multiply both sides by -1
y+=+0.36.........
now find x
4x=3.56+-+5y
x=+3.56%2F4+-+5%280.36%29%2F4
x=+0.89+-+1.25%280.36%29
x=+0.89+-+0.45

x=+0.44

check:
4%280.44%29+%2B+5%280.36%29+=3.56

1.76%2B+1.8+=3.56
3.56+=3.56