Question

Chau's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Chau $5.50 per pound, and type B coffee costs $4.20 per pound. This month, Chau made 143 pounds of the blend, for a total cost of $677.30. How many pounds of type B coffee did he use?

Answer 1

84 pounds of Type B coffee is used

Solution:

Let "x" be the pounds of type A coffee

Let "y" be the pounds of type B coffee

Cost per pound of type A = $ 5.50

Cost per pound of Type B = $ 4.20

This month, Chau made 143 pounds of the blend

x + y = 143

x = 143 - y -------- eqn 1

For a total cost of $677.30. Thus we frame a equation as:

pounds of type A coffee x Cost per pound of type A + pounds of type B coffee x Cost per pound of Type B = 677.30

$x \times 5.50 + y \times 4.20 = 677.30\\\\5.5x + 4.2y = 677.30 -------- eqn 2$

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

$5.5(143-y) +4.2y = 677.30\\\\786.5 -5.5y + 4.2y = 677.30\\\\5.5y - 4.2y = 786.5 - 677.30\\\\1.3y = 109.2\\\\Divide\ both\ sides\ by\ 1.3\\\\y = 84$

Thus 84 pounds of Type B coffee is used