SOLUTION: Colombian coffee beans cost $5.50/lb., while Peruvian coffee beans cost $4.25/lb. We want to mix the beans together so as to produce a 40-lb bag, costing $4.60/lb. How many pounds

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Colombian coffee beans cost $5.50/lb., while Peruvian coffee beans cost $4.25/lb. We want to mix the beans together so as to produce a 40-lb bag, costing $4.60/lb. How many pounds       Log On


   

Question 507607: Colombian coffee beans cost $5.50/lb., while Peruvian coffee beans cost $4.25/lb. We want to mix the beans together so as to produce a 40-lb bag, costing $4.60/lb. How many pounds of each type of bean should be used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = pounds of Columbian beans needed
Let b = pounds of Peruvian beans needed
given:
+5.5a+ = cost of Columbian beans in mixture
+4.25b+ = cost of Peruvian beans in mixture
(1) +a+%2B+b+=+40+
(2) +%285.5a+%2B+4.25b+%29+%2F+40+=+4.6+
---------------------
(2) +5.5a+%2B+4.25b+=+184+
(2) +550a+%2B+425b+=+18400+
Multiply both sides of (1) by +425+
and subtract (1) from (2)
(2) +550a+%2B+425b+=+18400+
(1) +-425a+-+425b+=+17000+
+125a+=+1400+
+a+=+11.2+
and, since
+a+%2B+b+=+40+
+11.2+%2B+b+=+40+
+b+=+28.8+
11.2 pounds of Columbian and 28.8 pounds of Peruvian
should be used
check answer:
(2) +%285.5%2A11.2+%2B+4.25%2A28.8+%29+%2F+40+=+4.6+
(2) +%28+61.6+%2B+122.4+%29+%2F+40+=+4.6+
(2) +184+%2F+40+=+4.6+
(2) +184+=+184+
OK