Question

Yoko's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Yoko $ 5.55 per pound, and type B coffee costs $ 4.30 per pound. This month, Yoko made 173 pounds of the blend, for a total cost of $ 866.40 . How many pounds of type B coffee did she use?

Answer 1

Answer: she should use 75 pounds of type B coffee.

Explanation:

Let x represent the number of pounds of Type A coffee that Yoko should use.

Let y represent the number of pounds of Type B coffee that Yoko should use.

The blend is a mixture of Type A and Type B coffee. Type A coffee costs Yoko $ 5.55 per pound, and type B coffee costs $ 4.30 per pound. The total cost of the blend is $866.40. This means that

5.55x + 4.3y = 866.40 - - - - - - - - 1

Yoko made 173 pounds of the blend. This means that

x + y = 173

Substituting x = 173 - y into equation 1, it becomes

5.55(173 - y) + 4.3y = 866.40

960.15 - 5.55y + 4.3y = 866.40

- 5.55y + 4.3y = 866.40 - 960.15

-1.25y = - 93.75

y = - 93.75/-1.25

y = 75

x = 100 - y

x = 100 - 75 = 25