Question

If 10 bags of jelly beans and 6 licorice sticks cost $1, and 10 licorice sticks and 6 jelly bean bags cost 92 cents.

How much does one licorice stick cost?

Answer 1

Here both the bags of jelly bean and licorice can be taken as unknowns on LHS of the equation and the cost can be taken on the RHS of the equation as shown below on both cases.

So each stick of Licorice costs 5 cents
And each bag of jelly bean costs 7 cents which can be found out by substitution of licorice value in any of the 3 equation mentioned in the image above.

Answer 2

Let the cost of a bag of jelly beans be "B"
Let the cost of a liquorice stick be "L"
Then:
(1) 6B + 10L = $0.92
(2) 10B + 6L = 1.00
Multiply equation (1) by 10 and equation (2) by 6
Now you have:
(1) 60B + 100L = $9.20
(2) 60B + 36L = 6.00
Now subtract equation (1) minus equation(2) .
The Jelly beans cancel out and you are left with and equation with one unknown to solve:
64L = $3.20
Divide both sides by 64 so you get what one liquorice stick costs L= $0.05
Cost of one licorice stick is 5 cents!