SOLUTION: If 5 pounds of sugar and 8 pounds of coffee cost $50.64, and at the same price 9 pounds of sugar and 12 pounds of coffee cost $76.80, how much per pound does the sugar cost? The co

Algebra ->  Square-cubic-other-roots -> SOLUTION: If 5 pounds of sugar and 8 pounds of coffee cost $50.64, and at the same price 9 pounds of sugar and 12 pounds of coffee cost $76.80, how much per pound does the sugar cost? The co      Log On


   

Question 1111426: If 5 pounds of sugar and 8 pounds of coffee cost $50.64, and at the same price 9 pounds of sugar and 12 pounds of coffee cost $76.80, how much per pound does the sugar cost? The coffee?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = cost/pound of coffee
Let +b+ = cost/pound of sugar
-----------------------------------
(1) +8a+%2B+5b+=+50.64+
(2) +12a+%2B+9b+=+76.80+
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(1) +800a+%2B+500b+=+5064+
Multiply both sides by +3+
(1) +2400a+%2B+1500b+=+15192+
and
(2) +1200a+%2B+900b+=+7680+
Multiply both sides of (2) by +2+
and subtract (1) from (2)
(2) +2400a+%2B+1800b+=+15360+
(1) +-2400a+-+1500b+=+-15192+
-----------------------------------
+300b+=+168+
+b+=+.56+
and
(1) +8a+%2B+5b+=+50.64+
(1) +8a+%2B+5%2A.56+=+50.64+
(1) +8a+=+50.64+-+2.8+
(1) +8a+=+47.84+
(1) +a+=+5.98+
Coffee is $5.98/pound
Sugar is $.56/pound
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check:
(1) +8a+%2B+5b+=+50.64+
(1) +8%2A5.98+%2B+5%2A.56+=+50.64+
(1) +47.84+%2B+2.8+=+50.64+
(1) +50.64+=+50.64+
OK
You can check (2)