A store mixes red fescue worth $10 per pound and ryegrass worth $13 per pound. The mixture is to sell for $12 per pound. Find how much of each should be used to make a 120 pound mixture.
f+r = 120
10f+13r = 12*120
To solve this problem, we can use a system of equations. Let's define the variables:
Let x represent the amount of red fescue (in pounds) used in the mixture.
Let y represent the amount of ryegrass (in pounds) used in the mixture.
We have two pieces of information:
1. The total weight of the mixture is 120 pounds:
x + y = 120
2. The price per pound of the mixture is $12:
(10x + 13y) / 120 = 12
Now, we can solve these equations simultaneously to find the values of x and y.
To solve equation 1 for x, we can subtract y from both sides:
x = 120 - y
Now substitute this expression for x in equation 2:
(10(120 - y) + 13y) / 120 = 12
Simplify and solve for y:
(1200 - 10y + 13y) / 120 = 12
1200 + 3y = 1440
3y = 240
y = 80
Now, substitute the value of y back into equation 1 to find x:
x + 80 = 120
x = 40
Therefore, to make a 120-pound mixture, you should use 40 pounds of red fescue and 80 pounds of ryegrass.