Question 717756
Knowns:
a) peanuts cost $3/lb
b) cashews cost $6/lb
c) mixture uses 12lb of peanuts
d) the mixture costs $4.20/lb
Unknown:
1) how many pounds of cashews are needed?
Let c = number of pounds of cashews
What relationship do we use get c?
"The cost of the peanuts plus the cost of the cashews equals the cost of the mixture", wherein the cost is the product of the cost per pound and the number of pounds. This relationship gives us the following equation,
(1) 3*12 + 6*c = 4.20*(12 + c) or
(2) 36 + 6*c = 50.4 + 4.2*c or
(3) 1.8*c = 14.4 or
(4) c = 8
Let's check this using (1).
Is (3*12 + 6*8 = 4.2*(12 + 8))?
Is (36 + 48 = 4.2*20)?
Is (84 = 84)? Yes
Answer: Use 8 pounds of cashews.