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

02-07-2018
Mathematics

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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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perixwinkle perixwinkle · Answer 1 · 2018-07-02T19:25:45+02:00

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.