Mixed nuts. Oh Nuts! sells pistachio kernels for $6.50 per pound and almonds for $8.00 per pound. How much of each type should be used to make a 50-lb mixture that sells for $7.40 per pound?
let the amount of pistastio be x
let the amount of almonds be 50-x
solve
6.5x + 8(50-x) = 7.4(50)
X= $20
To solve this problem, we need to set up a system of equations. Let's assume the amount of pistachio kernels used is x pounds, and the amount of almonds used is y pounds.
The total weight of the mixture is 50 pounds, so we can write the first equation as:
x + y = 50
Next, we need to consider the cost of the mixture. The cost per pound of pistachio kernels is $6.50, and the cost per pound of almonds is $8.00. The cost of the mixture per pound is $7.40. We can write the second equation as:
(6.50x + 8.00y) / 50 = 7.40
To solve this system of equations, we can use substitution or elimination method. Let's solve it using the substitution method.
1. Solve the first equation for x:
x = 50 - y
2. Substitute the value of x into the second equation:
(6.50(50 - y) + 8.00y) / 50 = 7.40
(325 - 6.50y + 8.00y) / 50 = 7.40
3. Simplify the equation:
(325 + 1.50y) / 50 = 7.40
4. Multiply both sides of the equation by 50 to eliminate the denominator:
325 + 1.50y = 370
5. Subtract 325 from both sides:
1.50y = 45
6. Divide both sides by 1.50:
y = 30
Now we know that y (the amount of almonds used) is 30 pounds.
7. Substitute the value of y back into the first equation to find x:
x + 30 = 50
x = 20
Therefore, to make a 50-pound mixture that sells for $7.40 per pound, you should use 20 pounds of pistachio kernels and 30 pounds of Almonds.