SOLUTION: Six apples and three oranges cost $3.36. Two apples and five oranges cost $3.04. Find the cost of an apple and the cost of an orange.

Algebra ->  Linear-equations -> SOLUTION: Six apples and three oranges cost $3.36. Two apples and five oranges cost $3.04. Find the cost of an apple and the cost of an orange.      Log On


   

Question 4850: Six apples and three oranges cost $3.36. Two apples and five oranges cost $3.04. Find the cost of an apple and the cost of an orange.
Found 2 solutions by rapaljer, Abbey:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = number of apples
y = number of oranges

6x + 3y = $3.36
2x + 5y = $3.04

The easiest way to eliminate a variable is to multiply both sides of the second equation by -3.

6x + 3y = $3.36
-3(2x + 5y) = -3($3.04)

6x + 3y = $3.36
-6x - 15y = -9.12

Add the equations together:
-12y = -5.76

Divide by -12, and get y = $.48 per orange

Substitute y = .48
6x + 3y = $3.36
6x + 3(.48) = 3.36
6x + 1.44 = 3.36
6x = 1.92
x = $.32 per apple

Check both numbers in the second equation:
2x + 5y = $3.04
2(.32) + 5(.48) = 3.04
$.64 + $2.40 = $3.04
It checks!!

R^2 at SCC

Answer by Abbey(339) About Me  (Show Source):
You can put this solution on YOUR website!
Let the cost of apples be x
Let the cost of oranges be y
Then:
6x+3y=3.36
2x+5y=3.04
Multiply the first equation by -1/3
-2x+-y=-1.12
2x+5y=3.04
add the second equation to the first
4y=1.92
divide both sides by 4
y=.48
put this back into either of the original equations to find out how much an apples costs
6x+3y=3.36
6x+3(.48)=3.36
6x+1.44=3.36
6x=3.36-1.44
6x=2.92
x=.32
check this answer by using the other equation:
2x+5y=3.04
2(.32)+5(.48)=3.04
.64+2.40=3.04
This is true, so oranges cost .48 cents each and apples cost .32 cents each.