A seed company sells two grades of grass seed. A 100-pound bag of a mixture of rye and Kentucky 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?

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\begin{align*} & {\text{Let x = bag of mixture of rye and Kentucky blue grass}}\\ \\ & {\text{Let y = bag of blue grass}}\\ \\ & x+y=19 && {\text{Equation 1}}\\ \\ & 245x+347y=5369 && {\text{Equation 2}}\\ \\ & x+y-y=19-y && {\text{Isolate variable $x$}}\\ \\ & x=19-y && {\text{Simplify}}\\ \\ & 245(19-y)+347y=5369 && {\text{Substitute the value of $x$ in equation $2$}}\\ \\ & 4655-245+347y=5369 && {\text{Distribute the multiplication}}\\ \\ & 4655+102y=5369 && {\text{Combine like terms}}\\ \\ & 4655+102y-4655=5369-4655 && {\text{Use subtraction property of equality}}\\ \\ & 102y=714 && {\text{Simplify}}\\ \\ & \dfrac{\cancel{102}y}{\cancel{102}} = \dfrac{714}{102} && {\text{Use division property of equality}}\\ \\ & {\color{#4257b2}y=7} && {\text{Simplify}}\\ \\ & x+y=19 && {\text{Equation 1}}\\ \\ & x+7=19 && {\text{Substitute $7$ for $y$}}\\ \\ & x+7-7=19-7 && {\text{Use subtraction property of equality}}\\ \\ & {\color{#4257b2}x=12} && {\text{Simplify}}\\ \end{align*}

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