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.
