SOLUTION: Linear System Word Problems Please help me figure this out. The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each orang

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Question 152763: Linear System Word Problems
Please help me figure this out.
The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each orange and each apple.
Thank you
Ryan
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each orange and each apple.
;
Write an equation for each transaction; o=cost of ea orange; a=cost of each apple
12o + 7a = 5.36
8o + 5a = 3.68
:
Multiply the 2nd equation by 1.5 and subtract the 1st equation from it:
12o + 7.5a = 5.52
12o + 7a = 5.36
-------------------Subtraction eliminates o, find a
0o + .5a = 0.16
a =
a = .32 for each apple
:
Find o using eq: 8o + 5a = 3.68
8o + 5(.32) = 3.68
8o + 1.6 = 3.68
8o = 3.68 - 1.60
8o = 2.08
o =
o = .26 for each orange
:
:
Check solution in the 1st equation:
12(.26) + 7(.32) =
3.12 + 2.24 = 5.36; confirms our solution