SOLUTION: An apple costs the same as 2 oranges. Together, an orange and a banana cost $.10 more than an apple. Two oranges cost $.15 more Ghana banana. What is the cost for one of each fruit

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Question 563236: An apple costs the same as 2 oranges. Together, an orange and a banana cost $.10 more than an apple. Two oranges cost $.15 more Ghana banana. What is the cost for one of each fruit?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = cost of an apple
Let +b+ = cost of a banana
Let +c+ = cost of an orange
-----------------------
given:
(1) +a+=+2c+
(2) +b+%2B+c+=+a+%2B+.1+
(3) +2c+=+b+%2B+.15+
------------------
(3) +b+%2B+.15+=+2c+
(3) +b+=+2c+-+.15+
Substitute (1) and (3) into (2)
(2) +b+%2B+c+=+a+%2B+.1+
(2) +2c+-+.15+%2B+c+=+2c+%2B+.1+
(2) +3c+-+.15+=+2c+%2B+.1+
(2) +c+=+.1+%2B+.15+
(2) +c+=+.25+
and
(1) +a+=+2c+
(1) +a+=+2%2A.25+
(1) +a+=+.5+
and
(3) +b+=+2c+-+.15+
(3) +b+=+2%2A.25+-+.15+
(3) +b+=+.5+-+.15+
(3) +b+=+.35+
The cost of an apple is $.50
The cost of a banana is $.35
The cost of an orange is $.25
check:
(2) +b+%2B+c+=+a+%2B+.1+
(2) +.35+%2B+.25+=+.5+%2B+.1+
(2) +.6+=+.6+
OK
(3) +2c+=+b+%2B+.15+
(3) +2%2A.25+=+.35+%2B+.15+
(3) +.5+=+.5+
OK