College Algebra

Question

A store is having a sale on trail mix and jelly beans. For 2 pounds of trail mix and 5 pounds of jelly beans, the total cost is $18. For 8 pounds of trail mix and 3 pounds of jelly beans, the total cost is $21. Find the cost for each pound of trail mix and each pound of jelly beans.

Answer 1

You can solve this using (what I learned as) simultaneous equations. The basic idea is that we'll write 2 equations based on the given information. We'll solve one for one of the variables and then plug that solution into the other equation so that there is only one variable.

t = trail mix, j = jelly beans

2t + 5j = 18

8t + 3j = 21

Solving the first for t

2t = 18 - 5j

t = (18 - 5j)/2

Substituting

8(18-5j)/2 + 3j = 21

4(18-5j) + 3j = 21

72 - 20j + 3j = 21

72 - 17j = 21

-17j = -51

j = 3. Jelly beans cost $3/lb

Use that in either equation (it might be good to check that you get the same answer!)

8t + 3(3) = 21

8t + 9 = 21

8t = 12

t = 1.5, trailmix costs $1.5 dollars/lb (it might be good to plug this in to either equation to check that $3 for jelly beans is valid)

Spoiler alert, in both cases, these numbers work. Double checking is a good habit, however.