SOLUTION: 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.

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Question 551075: 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.
Answer by Maths68(1474) About Me  (Show Source):
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Let
Cost of one orange = r
Cost of one apple = a

12r+7a=5.36..........(1)
8r+5a=3.68...........(2)
Multiply (1) by 8 and (2) by 12 then subtract(2) from (1)
96r+56a=42.88
-96r-60a=-44.16
---------------
-4a=-1.28
-4a/-4=-1.28/-4
a=0.32
Put the value of a in (2)
8r+5a=3.68...........(2)
8r+5(0.38)=3.68
8r+1.6=3.68
8r=3.68-1.6
8r=2.08
8r/8=2.08/8
r=0.26

Cost of one orange = r = 0.26
Cost of one apple = a = 0.32

Check
=====
The cost of 12 oranges and 7 apples is $5.36
12r+7a=5.36..........(1)
12(0.26)+7(0.32)=5.36
3.12+2.24=5.36
5.36=5.36
Eight oranges and 5 apples cost $3.68
8r+5a=3.68...........(2)
8(0.26)+5(0.32)=3.68
2.08+1.60=3.68
3.68=3.68