SOLUTION: A grocer has two kinds of loose tea. One is worth $5 per pound and the other is worth $7 per pound. She mixes some of each kind of tea together to get a total of 50 pounds of a

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Question 732008: A grocer has two kinds of loose tea. One is worth $5 per pound and the other is worth $7 per pound.
She mixes some of each kind of tea together to get a total of 50 pounds of a mixed tea worth a total of $314.00.
Let
x = number of pounds of $5/pound tea in the mixture
y = number of pounds of $7/pound tea in the mixture
Use a system of equations that describes this situation to figure out how much of each kind of tea is in the mixture.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x = number of pounds of $5/pound tea in the mixture
y = number of pounds of $7/pound tea in the mixture
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(1) +x+%2B+y+=+50+
(2) +5x+%2B+7y+=+314+
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Multiply both sides of (1) by +5+
and subtract (1) from (2)
(2) +5x+%2B+7y+=+314+
(1) +-5x+-+5y+=+-250+
+2y+=+64+
+y+=+32+
and, since
(1) +x+%2B+y+=+50+
(1) +x+=+18+
18 pounds of $5/pound tea are needed
32 pounds of $7/pound tea are needed