Macario is making 14 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $8 per pound and almonds cost$4.75 per pound. How many pounds of almonds should Macario use for the mixture to cost $95.75 per pound to make.
add up the value of each part of the mix. Note that the $95.75 is the total cost, not the cost per pound.
4.75x + 8(14-x) = 95.75
To determine the number of pounds of almonds needed, we can use algebra.
Let's assume Macario uses "a" pounds of almonds.
According to the problem, Macario is making a total of 14 pounds of nut mixture with macadamia nuts and almonds.
Therefore, the weight of macadamia nuts used will be the total weight of the mixture (14 pounds) minus the weight of almonds used (a pounds):
Macadamia nuts weight = 14 - a
The cost of macadamia nuts is $8 per pound, and the cost of almonds is $4.75 per pound.
The total cost of the mixture is $95.75 per pound, considering the cost of macadamia nuts and almonds.
To calculate the total cost, we can multiply the cost per pound by the pounds used:
Cost of macadamia nuts = (Weight of macadamia nuts) x (Cost per pound of macadamia nuts) = (14 - a) x 8
Cost of almonds = (Weight of almonds) x (Cost per pound of almonds) = a x 4.75
The total cost of the mixture is equal to the sum of the costs of macadamia nuts and almonds:
Total cost = Cost of macadamia nuts + Cost of almonds
According to the problem, the total cost should be $95.75 per pound:
Total cost = 95.75
Now we can set up an equation using the values we have:
(14 - a) x 8 + a x 4.75 = 95.75
Let's solve this equation to find the value of "a".
To solve this problem, we need to set up an equation based on the given information.
Let's assume Macario uses x pounds of almonds in the mixture. Since he is making a total of 14 pounds of nut mixture, the weight of macadamia nuts would be (14 - x) pounds.
Now, let's calculate the cost of the macadamia nuts and almonds separately. Since macadamia nuts cost $8 per pound, the cost of macadamia nuts would be (14 - x) * $8. Similarly, the cost of almonds would be x * $4.75.
The total cost of the nut mixture would be the sum of the costs of macadamia nuts and almonds. We know that the total cost should be $95.75, so our equation becomes:
(14 - x) * $8 + x * $4.75 = $95.75
Now we can solve this equation to find the value of x.
(14 - x) * $8 + x * $4.75 = $95.75
112 - 8x + 4.75x = 95.75
112 - 95.75 = 3.25x
16.25 = 3.25x
x = 16.25 / 3.25
x = 5
Therefore, Macario should use 5 pounds of almonds in the mixture to make it cost $95.75.