Macario is making12 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $9 per pound and almonds cost $4.25 per pound. How many pounds of almonds and how many pounds of macadamia nuts should Macario use for the mixture to cost $74.75 to make.
Your choice... one variable or two?
If you wish to use two variables...
Let x represent the almonds and y the macadamia nuts.
x + y = 12
4.25x + 9y = 74.75
Now if I was you I would re-arrange for x from the first equation and sub it into the second equation and solve for y
x = 12 - y then sub that into 4.25x + 9y = 74.75, that is
4.25(12-y) + 9y = 74.75
once you have y sub it back into one of the original equations and solve for x : )
To solve this problem, let's assume that Macario uses x pounds of macadamia nuts and y pounds of almonds.
The total cost of the macadamia nuts will be 9x dollars, and the total cost of the almonds will be 4.25y dollars.
Since the total cost of the mixture is $74.75, we can write the equation:
9x + 4.25y = 74.75
We also know that Macario is making 12 pounds of nut mixture, so we can write another equation:
x + y = 12
To solve this system of equations, we can use the method of substitution.
First, we solve the second equation for x:
x + y = 12
x = 12 - y
Now we substitute this value of x into the first equation:
9(12 - y) + 4.25y = 74.75
Distributing and simplifying:
108 - 9y + 4.25y = 74.75
Combine like terms:
-4.75y = -33.25
Divide both sides by -4.75:
y = 7
Now we substitute this value of y back into the second equation to find x:
x + 7 = 12
Subtract 7 from both sides:
x = 5
Therefore, Macario should use 5 pounds of macadamia nuts and 7 pounds of almonds to make the mixture cost $74.75.