Solving a word problem using a system of linear equations of the form Ax + By = C

Question

A store is having a sale on trail mix and jelly beans. For 2 pounds of trail mix and 3 pounds of jelly beans, the total cost is $11. For 6 pounds of trail mix and 5 pounds of jelly beans, the total cost is $23. Find the cost for each pound of trail mix and each pound of jelly beans.

Answer 1

2T + 3J = 11

6T + 5J = 23

6T + 9J = 33

6T + 5J = 23

4J = 10

J = 10/4 = 5/2 = $2.50 per pound for Jelly beans

T = (11 - (3(5/2))/2 = 11/2 - 15/4 = 7/4 = $1.75 per pound for Trail Mix