Question

Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of 97.50. Jacob went into the same movie theater and bought 5 bags of popcorn and 4 drinks, costing a total of 51.50. Determine the price of each bag of popcorn and the price of each drink.

Answer 1

You can solve this question by setting up a system of equations.

First, assign variables to your unknown information.

• The price of popcorn bags:
  `x`
• The price of drinks:
  `y`

Next, set up your two equations using the variables:

Liam: 9x + 8y = 97.50

Jacob: 5x + 4y = 51.50

Now, there are two ways to solve this system of equations:

1. Substitution
2. Elimination

For this problem, let's use elimination. The elimination tactic, requires for one of the variables to be canceled out. That can only occur if they have the same coefficient. We can manipulate one of the equations so that the coefficient matches another.

Multiply Jacob's equation by 2, leaving you with a new equation of

10x + 8y = 103.0

Subtract Liam's equation from Jacob's new equation *be mindful of the negative symbol, as it will change the signs within the parenthesis*:

10x + 8y = 103.0

- (9x + 8y = 97.50)

The 8y should cancel out, leaving you wit x = 5.50

Now that you have x, the price of popcorn, you can plug this value into either equation and solve for y, the price of drinks.

Let's use Jacob's old equation.

5 (5.50) + 4y = 51.50

* multiply 5 and 5.5 to get 27.5, then subtract 27.5 from both sides of the equation*

4y = 24

*divide 4 from both sides of the equation*

y = 6

The price of popcorn was $5.50

The price of drinks was $6

You can check your answer by plugging y and x into Liam's equation.