mixing word problem

Question

A shop is mixing assorted nuts with dried fruit to create trial mix. If the nuts sell for $6 a  pound and the dried fruit sells for $4 a pound, how many pounds of each should be mixed to get 20 pounds of trail mix that sells for $5.25 a pound?

Answer 1

Let N = pounds of assorted nuts

Let F = pounds of dried fruit  

 

We want 20 pounds of trail mix  ==>  N + F = 20  ==>  F = 20 - N

 

We want the 20 pounds to sell for $5.25 a pound which is a total of $105, and the nuts sell for $6 a pound and the dried fruit sells for $4 a pound, so 

 

6N + 4F = 105  

 

Substitute the value for F in to this equation to get 

 

6N + 4(20 - N) = 105

6N +80 - 4N = 105

2N = 25

N = 25/2 = 12.5 pounds

 

So F = 20 - N = 20 - 12.5 = 7.5 pounds

 

The shop should mix 12.5 pounds of nuts with 7.5 pounds of dried fruit  

 

Check:  12.5 + 7.5 = 20 pounds total

            $6(12.5) + $4(7.5) = $75 + $30 = $105 = $5.25 a pound for 20 pounds