Question

A store is having a sale on jelly beans and trail mix. For 3 pounds of jelly beans and 5 pounds of trail mix, the total cost is $17. For 9 pounds of jelly beans and 7 pounds of trail mix, the total cost is $37. Find the cost for each pound of jelly beans and each pound of trail mix.

Answer 1

Let's start by defining some variables:
- Let j be the cost per pound of jelly beans
- Let t be the cost per pound of trail mix

We can use these variables to write two equations based on the information given in the problem:
3j + 5t = 17 (for 3 pounds of jelly beans and 5 pounds of trail mix)
9j + 7t = 37 (for 9 pounds of jelly beans and 7 pounds of trail mix)

We now have a system of two equations with two variables. We can solve for j and t using any method of our choice (substitution, elimination, etc.). Here, we'll use elimination by multiplying the first equation by 3 and the second equation by -1, then adding them together:

9j + 15t = 51
-9j - 7t = -37
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8t = 14

Dividing both sides by 8, we get t = 1.75. Now we can substitute this value back into one of the original equations (let's use the first one) to solve for j:

3j + 5(1.75) = 17
3j + 8.75 = 17
3j = 8.25
j = 2.75

Therefore, the cost per pound of jelly beans is $2.75 and the cost per pound of trail mix is $1.75.