Question

A store is having a sale on trail mix and jelly beans. For 5 pounds of trail mix and 6 pounds of jelly beans, the total cost is $35. For 3 pounds of trail mix and 2 pounds of jelly beans, the total cost is $15 . Find the cost for each pound of trail mix and each pound of jelly beans.

Answer 1

`t = 2.5 \\ j = 3.75`

Explanation:

`5t + 6j = 35 \\ 3t + 2j = 15 = > 2j = 15 - 3t \\ \\ 5t + 3(15 - 3t) = 35 \\ 5t + 45 - 9t = 35 \\ - 4t + 45 = 35 \\ - 4t = - 10 \\ 4t = 10 \\ t = 2.5 \\ \\ 3(2.5) + 2j = 15 \\ 7.5 + 2j = 15 \\ 2j = 7.5 \\ j = 3.75`

Check:

`5t + 6j = 35 \\5(2.5) + 6(3.75) = 35 \\ 12.5 + 22.5 = 35 \\ 35 = 35 \\ \\ 3t + 2j = 15 \\ 3(2.5) + 2(3.75) = 15 \\ 7.5 + 7.5 = 15 \\ 15 = 15`