Question

A 13​-pound mixture of coffee that contains both decaffeinated and regular coffee costs ​$34. The decaffeinated coffee costs ​$2 per​ pound, and the regular coffee costs ​$3 per pound. ​(a) Let x be the weight of the decaffeinated coffee and y be the weight of the regular coffee. Write a system of equations whose solution gives the amount of each type of coffee in the mixture. ​(b) Use the method of substitution to solve the system of equations.

Answer 1

Weight of decaf coffee = 5 pounds.

Weight of regular coffee = 8 pounds.

Explanation:

(a) Let x be the weight of decaf coffee and y the weight of regular coffee. Then:

x + y = 13

2x + 3y = 34

(b) From the first equation x = 13 - y, so substituting for x in second equation:

2(13 - y) + 3y = 34

26 - 2y + 3y = 34

y = 34 - 26 = 8.

Substituting for y in the first equation:

x + 8 = 13

x = 5.