Question

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?

Answer 1

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