A sporting goods store has added a section with trail foods and snacks. Raisins cost $5.00 per pound and peanuts cost $3.80 per pound. Raisins and peanuts are going to be sold in a mixture of 30 pounds which will cost $4.05 per pound. How many pounds of raisins will be in the mix?

Question

Mathematics

Chippy

1 June, 12:36

A sporting goods store has added a section with trail foods and snacks. Raisins cost $5.00 per pound and peanuts cost $3.80 per pound. Raisins and peanuts are going to be sold in a mixture of 30 pounds which will cost $4.05 per pound. How many pounds of raisins will be in the mix?

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Answers (1)

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Tess Branch · Answer 1

Let's find the total cost of the mixture.

4.05*30

121.50

r=raisins; p=peanuts.

We need to make a system of equations.

r+p=30; this represents the pounds.

5r+3.8p=121.50; this represents the cost.

We can multiply the first equation by - 5 to eliminate r.

-5r-5p=-150

5r+3.8p=121.50

-1.2p=-28.5

Let's divide.

-28.5:-1.2

P=23.75

If there are 23.75 pounds of peanuts, there has to be 6.25 pounds of raisins. Let's check.

23.75 (3.80) + 6.25 (5)

90.25+31.25

121.5

So, there will be 6.25 pounds of raisins.