Question

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?

Answer 1

HI THERE!
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let the number of raisins (in pounds) be R and the number of peanuts (in pounds be p.

since the bag is 30 pounds, so R+P =30
the total cost of the bag is 30 pounds* 4.05 per pound = $121.50 .
now we can use the per-pound costs to write an equation . . .
5R+3.8P=121.5

Now just solve that first equation. . (R+P=30) for R. R= 30- P


now use that to substitute in the other equation
5R+3.8P=121.5
5(30-p) + 3.8P=121.5
solve for p
150- 5P+ 3.8p = 121.5
150-1.2p=121.5
150-1.2p=121.5
-1.2p=-28.5
P=23.75

now use that to find r
R+p =30
r+23.75=30
R=6.25



(hope this helps sorry it took so long to type )
have a good day !