The complete solution with step?

Question

You plan to create a mixture of nuts for the holiday season. You want to mix cashews and walnuts to sell for $2 per pound. Walnuts cost $1.50 per pound and cashews cost $3 per pound. If you want to have a total of 60 pounds of your mixture, then how many pounds of cashews and how many pounds of walnuts must you buy to sell your mixture at $2 per pound?

Answer 1

cashew=x pounds

wallnuts=60-x pounds

so, cost of cashew=$ 3x

cost of wallnut= $1.5[60-x]=$[90-1.5x]

total cost=$120

Hence, 3x+90-1.5x=120

==> 1.5x=30

==> x= 30/1.5=20

So, quantity of cashew=20 pounds

quantity of wallnuts=40 pounds

Answer 2

Let:

x = quantity of walnuts

y = quantity of cashew nuts

1. x + y = 60

2. 1.5x + 3y = 2(60) = 120

Multiplying Eq. 2 by 2:

3. 3x + 6y = 240

Multiplying Eq. 1 by 3;

4. 3x + 3y = 180

Subtract Eq. 4 fom Eq. 3

5. 3y = 60

y = 20 lbs

x = 60 - 20 = 40 lbs