Question

Cashews cost $2.50 per pound. Peanuts cost $5 per pound. Steven wants a mixture of cashews and peanuts that costs $4.50 per pound and weighs 10 pounds. How many pounds of cashews and how many pounds of peanuts are needed to make this mixture?

Answer 1

So let's form some equations
Let C = Cashews and P = Peanuts

The weight of C and P is equal to 10 pounds.
C + P = 10

The mixture costs $4.50 per pound which is $45 for 10 pounds.
2.5C + 5P = 45

Now you see that they are simultaneous equations. Use either elimination or substitution to solve them. I'm gonna use substitution
1. C + P = 10
2. 2.5C + 5P = 45
From equation 1, C = 10 - P
Substitute into equation 2
2.5(10-P) + 5P = 45
25 - 2.5P + 5P = 45
2.5P=20
P=20/2.5 = 8

Now resubstitute into 1 to find C
C + 8 = 10
C = 2

Answer 2

Thank you for your help.