how many pounds of $4.60 per pound nuts to be mixed with 8 pounds of $3.75 per pound nuts make a mixture worth $3.92 a pound?

Question

Help me to resolve this problem please

Answer 1

Let's let N be the number of pounds of $4.60/lb nuts needed.

We know that the total cost of the mixture will be $3.92/lb with 8lbs priced at $3.75. So we know that the total cost of the mixture will be:

8($3.75) + N($4.60)

We also know that the per pound price will be:

[ 8($3.75) + N($4.60) ] / (8 + N) = $3.92.

Now let's solve for N:

8($3.75) + N($4.60) = (8 + N)($3.92)

So $30.00 + N($4.60) = 8($3.92) + N($3.92)

Then $30.00 + N($4.60) = $31.36 + N($3.92)

So N($4.60 - $3.92) = $31.36 - $30.00

N($0.68) = $1.36

N = $1.36 / $0.68 = 2

So 2lbs of nuts priced at $4.60/lb are needed.