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Rachel's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Rachel $4.30 per pound, and type B coffee costs $5.90 per pound. This month, Rachel made 148 pounds of the blend, for a total cost of $738.80. How many pounds of type B coffee did she use?

User Gigisommo
by
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1 Answer

1 vote

Step 1

Write out the system of equations


let\text{ x represent pound of Type A coffee and y represent Type B coffee pound }
\begin{gathered} 4.30x+5.9y=738.80----(1) \\ x+y=148---(2) \end{gathered}

Step 2

Find the value of one pound of type A coffee, x


\begin{gathered} From\text{ equation 2; x+y=148} \\ Therefore \\ y=148-x \end{gathered}
\begin{gathered} Substitute\text{ for y in equation 1} \\ 4.30x+5.9(148-x)=738.80 \\ 4.30x+873.2-5.9x=738.80 \\ 873.2-738.80=5.9x-4.3x \\ 134.4=1.6x \\ x=84pounds \end{gathered}

Therefore the answer will be;


\begin{gathered} x+y=148 \\ 84+y=148 \\ y=64\text{ pounds} \\ \end{gathered}

The pounds of type B coffee she used is 64pounds

The pounds of type A coffee she used is 84 pounds

User Yusuke Kawabata
by
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