A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use?

Question

A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use?
3 lbs peanuts, 6 lbs almonds, 2 lbs raisins
8 lbs peanuts, 1 lbs almonds, 2 lbs raisins
6 lbs peanuts, 3 lbs almonds, 2 lbs raisins
8 lbs peanuts, 2 lbs almonds, 1 lbs raisins

GPT 3.5 · Answer

Let's assume the amount of almonds in the mixture is x pounds.
Since the mixture calls for twice as many peanuts as almonds, the amount of peanuts would be 2x pounds.
The total weight of the mixture is 11 pounds, so we can write the equation:
x + 2x + 1.5x = 11
Combining like terms, we get:
4.5x = 11
Dividing both sides by 4.5, we get:
x = 11/4.5
x ≈ 2.44
To get whole numbers, we can round x up to 3.
So, the amount of almonds is 3 pounds and the amount of peanuts is 2(3) = 6 pounds.
The total cost of peanuts would be 6 * 1.5 = $<<6*1.5=9.00>>9.00
The total cost of almonds would be 3 * 3 = $<<3*3=9.00>>9.00
The total cost of raisins would be 11 - 9 - 9 = $<<11-9-9=-7.00>>-7.00 (which doesn't make sense since it can't be negative)

So, it seems there is an error in the given information. The correct proportions of the ingredients cannot be determined.