SOLUTION: Thirty pound of dried fruit mix contained apples worth #3.15 a pound and pears worth $4.25 a pound. How many pounds of each did the mix contain if the value of the mix was $107.70?

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Question 731619: Thirty pound of dried fruit mix contained apples worth #3.15 a pound and pears worth $4.25 a pound. How many pounds of each did the mix contain if the value of the mix was $107.70?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of apples needed
Let +b+ = pounds of pears needed
given:
(1) +a+%2B+b+=+30+
(2) ++3.15a+%2B+4.25b+=+107.7+
----------------------------
(2) +315a+%2B+425b+=+10770+
Multiply both sides of (1) by +315+
and subtract (1) from (2)
(2) +315a+%2B+425b+=+10770+
(1) +-315a+-+315b+=+-9450+
+110b+=+1320+
+b+=+12+
and, since
(1) +a+%2B+b+=+30+
(1) +a+=+18+
18 pounds of apples and 12 pounds of pears are needed
check:
(2) +3.15a+%2B+4.25b+=+107.7+
(2) +3.15%2A18+%2B+4.25%2A12+=+107.7+
(2) +56.7+%2B+51+=+107.7+
(2) +107.7+=+107.7+
OK