A seed company sells two grades of seed. A 100-pound bag of a mixture of rye and Kentucky bluegrass sells for $235, and a 100-pound bag of bluegrass sells for $341. How many bags of each are sold in a week when the receipts for 17 bags are $4,949?

Answer:The company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrassStep-by-step explanation:This is a classical problem that can be solved using a system of equations:Let us first define our variables:[tex]x[/tex] as the number of 100-pound bags which contain a mixture of rye and Kentucky bluegrass and,[tex]y[/tex] as the number of 100-pound bags of bluegrass.The problem tells us that in a week a total of 17 bags were sold, therefore, we can say that this number must be equal to the number of bags containing the mixture of rye and Kentucky bluegrass plus the number of bags containing bluegrass. Then, according to our variable names:[tex]x+y=17[/tex]   (1)The problem also says that the company got a receipt for $4,949 in total. Hence, this number has to be equal to the total number of bags that contain rye and Kentucky bluegrass seeds times its price plus the number of bags containing bluegrass multiplied by its price. Then,[tex]235x+341y=4949[/tex]  (2)Now we have the system of equations:[tex]x+y=17[/tex]   (1)[tex]235x+341y=4949[/tex]  (2)Solving for [tex]x[/tex] in equation (1)[tex]x+y=17\\x=17-y[/tex]   (3)And substituting [tex]x[/tex] in equation (2)[tex]235x+341y=4949\\235(17-y)+341y =4949\\3995 - 235y +341y=4949\\-235y+341y = 4949-3995\\106y=954\\y=\frac{954}{106}\\ y=9[/tex]Then, substituting [tex]y=9[/tex] in equation (1):[tex]x+y=17\\x+9=17\\x=17-9\\x=8[/tex]Thus, the company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass.