A store mixes red fescue worth $12 per pound and chewings fescue worth $16 per pound. The mixture is to sell for $15 per pound. Find out how much of each should be used to make a 552 - pound mixture.

Question

Mathematics

Ayanna Guerra

17 February, 02:01

A store mixes red fescue worth $12 per pound and chewings fescue worth $16 per pound. The mixture is to sell for $15 per pound. Find out how much of each should be used to make a 552 - pound mixture.

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Answers (1)

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Cadence Simpson · Answer 1

Answer is: 414 pounds of red fescue and 138 pounds of chewings fescue is needed to produce 552 pounds of mixture.

Explanation:

x - how much of red fescue is needed for one pound of mixture

y - how much of chewings fescue is needed for one pound of mixture x*12 + y*16 = 15 x + y = 1

so, x=1-y

putting it into first line: (1-y) * 12 + y*16 = 15

12 - 12*y + 16*y = 15

4*y = 3

y=3/4

so, x = 1-3/4; x=1/4 So to produce 552 pounds of mixture we need ... To produce 1 pound of mixture we need: 3/4 pound of red fescue and 1/4 pound of chewing fescue so to produce 552 pounds of miture we need:

552*3/4 - red fescue, which is 414 pounds needed

and

552/4 - chewings fescue, which is 138 pounds needed