a store mixes red fescue worth $10 per pound and ryegrass worth $14 per pound. The mixture is to sell for $13 per pound. Find out how much of each should be used
to make a 228-pound mixure
To find out how much of each type of grass should be used to make a 228-pound mixture that sells for $13 per pound, we can set up a system of equations.
Let's assume the store uses x pounds of red fescue and y pounds of ryegrass.
The first equation represents the total weight of the mixture:
x + y = 228
The second equation represents the value of the mixture:
10x + 14y = 13 * 228
To solve this system of equations, we can use the substitution method or the elimination method.
Using the substitution method, we can solve for x in the first equation:
x = 228 - y
Substitute x in the second equation:
10(228 - y) + 14y = 13 * 228
2280 - 10y + 14y = 2964
4y = 2964 - 2280
4y = 684
y = 684/4
y = 171
Substitute y back into the first equation to solve for x:
x + 171 = 228
x = 228 - 171
x = 57
Therefore, the store should use 57 pounds of red fescue and 171 pounds of ryegrass to make a 228-pound mixture that sells for $13 per pound.