The document discusses using a bar model method to solve two-step equations. It provides an example of an equation representing the costs of a class trip, with variable x representing the price of individual passes. A bar model is created showing the equation x + x + 11 = 52, with the top bar representing the costs of the two passes (x + x) and concert ticket (11), and the bottom bar the total cost (52). The equation is then solved by first subtracting 11 from both sides, then dividing the remaining amount (41) by 2 since there are two x values, to find that x = $20.50.

1. Bar Model
Algebraic equations include a variable. A variable is a letter that represents an
unknown number. A variable could represent a single amount, such as the number of
Tommy’s pencils, or a combined amount, such as the amount of Tommy’s pens and
pencils. In order to solve equations, it’s important to understand what the variable
represents.
The goal today is to teach you how to solve two step-step equations. There are a
variety of methods and strategies to solve these types of problems, but today we are going
to discuss one: the bar method. Remember that equations have an equal sign. It’s also
important to remember that everything on one side of the equal sign is equal to, or the same
as, everything on the other side of the equal sign. Let’s use the bar method to solve a
problem.
“Your class is going on a trip to the state fair. The trip costs $52. Included in that price is
$11 for a concert ticket and the cost of 2 passes, one for the rides and one for the games.
Each of the passes cost the same price. We could write an equation to represent the
situation, with x representing the price of each pass.”
Create a bar model to show this equation:
x + x + 11 = 52
2x + 11 = 52
The top bar includes 2 variables, x and x, to represent the 2 passes. The 11 represents the
price of the concert ticket. The bottom bar represents the total cost. Notice that the length of
the top and bottom bar are the same, because the two amounts are equal.
To solve, you first need to take away the cost of the concert ticket, which is $11.
Since the x values are equal, I can cut the 41 in half, or divide it by 2, which gives a total of
20.5. So x = $20.50