Question

Greg's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Greg $5.40 per pound, and type B coffee costs $4.05 per pound.

This month, Greg made 138 pounds of the blend, for a total cost of $675.00. How many pounds of type A coffee did he use?

Answer 1

Answer: the number of pounds of type A coffee that was mixed is 86

the number of pounds of type B coffee that was mixed is 52

Explanation:

Let x represent the number of pounds of type A coffee that was mixed.

Let y represent the number of pounds of type B coffee that was mixed.

Type A coffee costs Greg $5.40 per pound, and type B coffee costs $4.05 per pound.

This month, Greg made 138 pounds of the blend, for a total cost of $675.00. This means that

5.4x + 4.05y = 675 - - - - - - - - - 1

x + y = 138

Substituting x = 138 - y into equation 1, it becomes

5.4(138 - y) + 4.05y = 675

745.2 - 5.4y + 4.05y = 675

- 5.4y + 4.05y = 675 - 745.2

- 1.35y = - 70.2

y = - 70.2/-1.35

y = 52

x = 138 - y = 138 - 52

x = 86