Question

A store is having a sale on jelly beans and trail mix. For 8 pounds of jelly beans and 3 pounds of trail mix, the total is $18. For 2 pounds of jelly beans and 5 pounds of trail mix, the total cost is $13. Find the cost for each pound of jelly beans and each pound of trail mix.

Answer 1

Answer: each pound of jelly beans costs 1.5 dollars, or $1.50, and each pound of trail mix costs 2 dollars, or $2

Step-by-step explanation:

j = jellybeans

t = trail mix

2j + 5t = 13

8j + 3t = 18

To solve this, we want to isolate a variable, and solve for the other. Let's do that with each equation.

2j + 5t = 13

2j = 13 - 5t

j = (13 - 5t) / 2

8j + 3t = 18

8j = 18 - 3t

j = (18 - 3t) / 8

Now that we have isolated the variable j in each equation, we can set the two right-sides equal to each other, and solve for t.

(13 - 5t) / 2 = (18 - 3t) / 8

By multiplying both sides by 8, this becomes simpler to look at.

8 * (13 - 5t) / 2 = 18 - 3t

4 * (13 - 5t) = 18 - 3t

4 * 13 - 4 * 5t = 18 - 3t

52 - 20t = 18 - 3t

52 = 18 + 17t

34 = 17t

34 / 17 = t

t = 2

Now that we have solved for t, we can trivially plug it into one of the other equations to solve for j. Let's choose the first equation, as it doesn't matter which we choose.

t = 2

2j + 5t = 13

2j + 5 * 2 = 13

2j + 10 = 13

2j = 13 - 10

2j = 3

j = 1.5

So, each pound of jelly beans costs 1.5 dollars, or $1.50, and each pound of trail mix costs 2 dollars, or $2.