A store mixes peanuts worth $10 per pound and biscuit worth $13 per pound. The mixture is to sell for $12 per pound. Find how much of each should be used to make a 432 pound mixture.
10x + 13(432-x) = 12(432)
To find how much of each ingredient should be used to make a 432 pound mixture, we can set up a system of equations.
Let's assume x represents the number of pounds of peanuts, and y represents the number of pounds of biscuits.
We can set up the following equations:
Equation 1: x + y = 432 (since the total weight of the mixture is 432 pounds)
Equation 2: (10x + 13y) / 432 = 12 (since the average price per pound of the mixture is $12)
To solve this system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
Step 1: Solve Equation 1 for x in terms of y.
x = 432 - y
Step 2: Substitute x into Equation 2.
(10(432 - y) + 13y) / 432 = 12
Step 3: Simplify the equation.
(4320 - 10y + 13y) / 432 = 12
4320 + 3y = 5184
3y = 5184 - 4320
3y = 864
y = 864 / 3
y = 288
Step 4: Substitute the value of y back into Equation 1 to find x.
x + 288 = 432
x = 432 - 288
x = 144
Therefore, to make a 432 pound mixture, the store should use 144 pounds of peanuts and 288 pounds of biscuits.