A store sells mixtures of almonds and cashews for $6.50 per pound. Peanuts sell for $2.95 per pound and cashews sell for $7.95. How many pounds of each should be used to make 80 pounds of this mixture?
Assuming a typo, and you meant peanuts instead of almonds, we have
2.95p + 7.95(80-p) = 6.50*80
p = 23.2
So, 23.2 lbs of peanuts and 56.8 lbs of cashews
or whatever the nuts really are.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the number of pounds of almonds in the mixture is represented by "a", and the number of pounds of cashews is represented by "c".
Given:
1. The store sells mixtures of almonds and cashews for $6.50 per pound.
2. Peanuts sell for $2.95 per pound.
3. Cashews sell for $7.95.
From the given information, we can determine the following equations:
1. The total cost of the mixture (almonds + cashews) per pound is $6.50:
6.50 = (a + c) / 80
2. The total weight of the mixture (almonds + cashews) is 80 pounds:
a + c = 80
3. The cost per pound of peanuts is $2.95:
2.95 = a * 2.95
4. The cost per pound of cashews is $7.95:
7.95 = c * 7.95
Now, we can solve this system of equations step-by-step to find the values of "a" and "c".
Step 1: Simplify equation 3 and equation 4:
2.95 = a (Equation 3)
7.95 = c (Equation 4)
Step 2: Use equation 3 and equation 4 to substitute the values of "a" and "c" in equation 1:
6.50 = (a + c) / 80
6.50 = (2.95 + 7.95) / 80
Step 3: Combine like terms:
6.50 = 10.90 / 80
Step 4: Cross multiply:
(6.50 * 80) = 10.90
Step 5: Simplify:
520 = 10.90
Step 6: This equation is not true, which means the solution is not valid. There seems to be an error in the given information or the equations.
Based on the given information, it is not possible to determine the quantity of almonds and cashews needed to make a 80-pound mixture with a cost of $6.50 per pound.
To solve this problem, we can set up a system of equations based on the given information:
Let's assign variables to represent the unknown amounts of peanuts, almonds, and cashews in the mixture.
Let:
P = pounds of peanuts
A = pounds of almonds
C = pounds of cashews
We know that the total weight of the mixture is 80 pounds, so we can write the equation:
P + A + C = 80 (Equation 1)
Next, we can write the equation for the cost of the mixture. The cost depends on the price per pound for each ingredient. The price per pound for the mixture is $6.50, so the equation becomes:
2.95P + 6.50A + 7.95C = 6.50(80) (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) with three variables (P, A, and C). We need to solve for the values of P, A, and C.
To simplify Equation 2, we can distribute 6.50 to 80:
2.95P + 6.50A + 7.95C = 520
Now, we can solve this system of equations. There are multiple methods for doing this, but let's use the substitution method:
From Equation 1, we can solve for P:
P = 80 - A - C
Now, substitute this expression for P in Equation 2:
2.95(80 - A - C) + 6.50A + 7.95C = 520
Let's simplify and solve for A and C:
236 - 2.95A - 2.95C + 6.50A + 7.95C = 520
3.55A + 5.00C = 284 (Equation 3)
To continue solving for A and C, we need one additional equation. There are different approaches for obtaining another equation, but let's assume that the total weight of the mixture is fully comprised of peanuts, almonds, and cashews. So, we can add another equation:
P + A + C = 80
0 + A + C = 80
A + C = 80 (Equation 4)
Now we have two equations (Equation 3 and Equation 4) with two variables (A and C). We can solve these equations to find the values of A and C, and then determine the value of P using Equation 1.