Macario is making 9 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $8 per pound and almonds cost $5.25 per pound. How many pounds of almonds and how many pounds of macadamia nuts should Macario use for the mixture to cost $61.00 to make.
If there are x lbs of almonds, then the rest (9-x) is macadamias.
So, now just make sure the value of the parts adds up to the value of the mix:
5.25x + 8.00(9-x) = 61.00
To solve this problem, we can set up a system of equations to represent the given information. Let's use "x" to represent the number of pounds of macadamia nuts and "y" to represent the number of pounds of almonds.
From the problem, we know that Macario is making a total of 9 pounds of nut mixture. So, our first equation is:
x + y = 9 (equation 1)
We also know that macadamia nuts cost $8 per pound and almonds cost $5.25 per pound. The total cost of the mixture is $61.00. The cost of macadamia nuts used is 8x, and the cost of almonds used is 5.25y. Therefore, our second equation is:
8x + 5.25y = 61 (equation 2)
Now, we can solve this system of equations using substitution or elimination. Let's use substitution.
From equation 1, we can rearrange it to solve for x:
x = 9 - y (equation 3)
Now, substitute equation 3 into equation 2:
8(9 - y) + 5.25y = 61
Expand and simplify:
72 - 8y + 5.25y = 61
Combine like terms:
-2.75y = -11
Divide both sides by -2.75 to solve for y:
y = 4
Now that we have the value of y, substitute it back into equation 3 to find x:
x = 9 - 4 = 5
Therefore, Macario should use 5 pounds of macadamia nuts and 4 pounds of almonds for the mixture to cost $61.00 to make.