Question

A 14 ​-pound mixture of coffee that contains both decaffeinated and regular coffee costs ​$37. The decaffeinated coffee costs ​$2 per​ pound, and the regular coffee costs ​$3 per pound.

Answer 1

The number of pounds of:

Decaffeinated coffee = x = 5 pounds

Regular coffee = y = 9 pounds

Explanation:

A 14 ​-pound mixture of coffee that contains both decaffeinated and regular coffee costs ​$37. The decaffeinated coffee costs ​$2 per​ pound, and the regular coffee costs ​$3 per pound.

Let the number of pounds of:

Decaffeinated coffee = x

Regular coffee = y

Hence, our system of equations =

x + y = 14..... Equation

x = 14 - y

2x + 3y = 37....... Equation 2

We substitute 14 - y for x in Equation 2

= 2(14 - y) + 3y = 37

= 28 - 2y + 3y = 37

= - 2y + 3y = 37 - 28

= y = 9 pounds

Solving for x

x = 14 - y

x = 14 - 9

x = 5 pounds

Therefore,

The number of pounds of:

Decaffeinated coffee = x = 5 pounds

Regular coffee = y = 9 pounds