Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. macadamia nuts cost $9 per pound and almonds cost $5.25 per pound. how many pounds of macadamia nuts and how many pounds of almonds should macario use for the mixture to cost $6.50 per pound to make? The answer I have is 4 lbs of macadamia and 8 lbs of almond
where did the 150 come from? You only have 12 lbs of mix. And where did the cashews come from?
So, if x = macadamias, 12-x = almonds
That gives you an equation involving the cost of the nuts. The sum of the parts makes the value of the whole mix:
9x + 5.25(12-x) = 6.50(12)
x = 4, so 12-x = 8
thanks but im still confused, because I was trynna set it up like this
Let x be the number of pounds of cashews
So, 150 - x will represent the number of almonds
Since each pound of the mixture cost 3 dollars, 150 pounds will cost 3 × 150 = 450 dollars
Cost of cashews + cost of almonds = 450
2 × x + (150 - x) × 5 = 450
2x + 150 × 5 - x × 5 = 450
2x + 750 - 5x = 450
2x - 5x + 750 = 450
-3x + 750 = 450
-3x + 750 - 750 = 450 - 750
-3x = -300
-3x/-3 = -300/-3
x = 100
150 - x = 150 - 100 = 50.
it was an example. I was using to try to solve it also.
also where did you get the the negative 3.75 and 30
A store owner wants to mix cashews and almonds. Cashews cost 2 dollars per pound and almonds cost 5 dollars per pound. He plans to sell 150 pounds of a mixture. How many pounds of each type of nuts should be mixed if the mixture will cost 3 dollars?
Yo ooBleck, I understand now. I was distributing 5.25 into 12 -x but once I did that I kept forgetting a part of the problem. Math anxiety is really bad for me.
Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $9 per pound and almonds cost $5.25 per pound. How many pounds of macadamia nuts and how many pounds of almonds should Macario use for the mixture to cost $6.50 per pound to make?
To find out how many pounds of macadamia nuts and almonds Macario should use for the mixture to cost $6.50 per pound, we can start by setting up an equation.
Let's assume the number of pounds of macadamia nuts is "x" and the number of pounds of almonds is "y".
We know that the total weight of the mixture is 12 pounds, so we can write the equation:
x + y = 12
The cost per pound of macadamia nuts is $9 and the cost per pound of almonds is $5.25. We want the cost per pound of the mixture to be $6.50.
To calculate the cost per pound of the mixture, we need to find the total cost of macadamia nuts (x pounds at $9 per pound) and the total cost of almonds (y pounds at $5.25 per pound) and divide it by the total weight of the mixture (12 pounds). This equation can be written as:
(9x + 5.25y) / 12 = 6.50
Now we have two equations:
x + y = 12
(9x + 5.25y) / 12 = 6.50
To solve these equations simultaneously, we can use substitution or elimination. However, in this case, it is easier to use substitution.
Rearrange the first equation, x = 12 - y, and substitute it into the second equation:
(9(12 - y) + 5.25y) / 12 = 6.50
Simplify the equation:
(108 - 9y + 5.25y) / 12 = 6.50
(108 - 3.75y) / 12 = 6.50
Multiply both sides of the equation by 12 to eliminate the denominator:
108 - 3.75y = 6.50 * 12
108 - 3.75y = 78
Subtract 108 from both sides:
-3.75y = -30
Divide both sides by -3.75:
y = 8
Now that we have the value of y, substitute it back into one of the original equations:
x + 8 = 12
x = 4
So, the solution is x = 4 and y = 8. This means Macario should use 4 pounds of macadamia nuts and 8 pounds of almonds to make the mixture cost $6.50 per pound.
m + a = 12 ... -9 m - 9 a = -108
9 m + 5.25 a = 12 * 6.50 = 78
solve the system
adding equations to eliminate m ... -3.75 a = -30
solve for a , then substitute back to find m