Question

Shen's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Shen $5.65 per pound, and type B coffee costs $4.35 per pound.

This month, Shen made 132 pounds of the blend, for a total cost of $649.60. How many pounds of type A coffee did he use?

Answer 1

58 pounds

Explanation:

You want the number of pounds of type A coffee at $5.65 per pound that, together with type B coffee at $4.35 per pound, will make 132 pounds of coffee at a cost of $649.60.

Setup

We can write an equation for the total cost of the coffee as follows. Let 'a' represent the number of pounds of type A coffee in the mix. Then the number of pounds of type B coffee is (132-a), and the total cost of the mix is ...

5.65a +4.35(132 -a) = 649.60

Solution

Eliminating parentheses and combining terms, we have ...

1.30a +574.20 = 649.60

1.3a = 75.4 . . . . . . . . . . . . . subtract 574.20

a = 58 . . . . . . . . . . divide by 1.3

Shen used 58 pounds of type A coffee in the blend.