SOLUTION: a store mixes Kentucky bluegrass worth $11 per pound and ryegrass worth $14 per pound. the mixture is to sell for $12 per pound. Find how much of each should be used to make a 204-

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Question 581161: a store mixes Kentucky bluegrass worth $11 per pound and ryegrass worth $14 per pound. the mixture is to sell for $12 per pound. Find how much of each should be used to make a 204-pound mixture.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of bluegrass needed
Let +b+ = pounds of ryegrass needed
given:
(1) +a+%2B+b+=+204+
(2) +%28+11a+%2B+14b+%29+%2F+204+=+12+
--------------------------------
(2) +11a+%2B+14b+=+2448+
Multiply both sides of (1) by +11+
and subtract (1) from (2)
(2) +11a+%2B+14b+=+2448+
(1) +-11a+-+11b+=+-2244+
+3b+=+204+
+b+=+68+
and, since
(1) +a+%2B+b+=+204+
(1) +a+%2B+68+=+204+
(1) +a+=+204+-+68+
(1) +a+=+136+
136 pounds of bluegrass is needed
68 pounds of ryegrass is needed
check:
(2) +%28+11a+%2B+14b+%29+%2F+204+=+12+
(2) +%28+11%2A136+%2B+14%2A68+%29+%2F+204+=+12+
(2) +%28+1496+%2B+952+%29+%2F+204+=+12+
(2) +2448+%2F+204+=+12+
(2) +2448+=+12%2A204+
(2) +2448+=+2448+
OK