A seed company sells two grades of grass seed. A 100-pound bag of a mixture of rye and bluegrass sells for $245 and a 100-pound bag of bluegrass sells for $347. How many bags of each are sold in a week when the receipts for 19 bags are $5,369?
x and (19-x)
245 x + 347(19-x) = 5369
To solve this problem, we can set up a system of linear equations.
Let's represent the number of bags of the mixture of rye and bluegrass as "x",
and the number of bags of bluegrass as "y".
From the given information, we have the following equations:
Equation 1: The price of a bag of the mixture of rye and bluegrass is $245:
245x
Equation 2: The price of a bag of bluegrass is $347:
347y
Equation 3: The total receipts for 19 bags is $5,369:
245x + 347y = 5,369
Now, we can solve this system of equations to find the values of "x" and "y".
To do so, we need an additional equation. We can use the fact that the total number of bags sold in a week is 19. Hence, we have:
Equation 4: The total number of bags sold is 19:
x + y = 19
Now we have a system of two equations with two variables:
Equation 3: 245x + 347y = 5,369 (multiply this equation by -1 to simplify)
Equation 4: x + y = 19
Let's solve this system of equations using the method of substitution:
From Equation 4, we have x = 19 - y
Substituting x = 19 - y into Equation 3:
245(19 - y) + 347y = 5,369
4,655 - 245y + 347y = 5,369
102y = 714
y = 714 / 102
y = 7
Now, substitute y = 7 into Equation 4:
x + 7 = 19
x = 19 - 7
x = 12
So, 12 bags of the mixture of rye and bluegrass and 7 bags of bluegrass are sold in a week when the receipts for 19 bags are $5,369.