A girl buys a monthly bus​ pass, which entitles her to unlimited bus​ travel, for ​$33 per month. Without the pass each bus ride costs ​$1.50. How many rides per month would she have to take so that the cost of the rides without the bus pass is equal to the total cost of the rides with the bus​ pass? The number of rides at which the unlimited ride pass equals the cost of individual ride purchases is

Let's define the variables and set up an equation to solve the problem.

### Variables:
- Let $ x $ be the number of bus rides she takes per month.

### Cost without the bus pass:
- Each bus ride costs $1.50.
- Therefore, the total cost without the pass for $ x $ rides is $ 1.50x $.

### Cost with the bus pass:
- The cost of the bus pass is $33 per month.
- With the bus pass, she can take unlimited rides for $33, so the cost remains $33 regardless of the number of rides.

### Setting Up the Equation:
We want to find the number of rides ($ x $) at which the cost of riding without a bus pass equals the cost with the bus pass:

\[
1.50x = 33
\]

### Solving for $ x $:

\[
x = \frac{33}{1.50}
\]

Let's calculate $ x $:

\[
x = 22
\]

### Conclusion:
The number of rides per month at which the cost of individual rides equals the cost of the unlimited bus pass is **22 rides**.

If you have any questions or want further details, let me know!

### Related Questions:
1. What if the cost per ride was $2.00 instead of $1.50?
2. How much would she save if she took 30 rides in a month with the bus pass?
3. How many rides would she need to take to save money with the pass?
4. What if the cost of the bus pass increased to $40? How would this change the number of rides?
5. What is the break-even point if the cost per ride was reduced to $1?

**Tip:** When comparing costs, always set up equations to find the break-even point where two options become equivalent.

A girl buys a monthly bus​ pass, which entitles her to unlimited bus​ travel, for ​$33 per month. Without the pass, each bus ride costs ​$1.50. How many rides per month would she have to take so that the cost of the rides without the bus pass is equal to the total cost of the rides with the bus​ pass?

Learn how to determine the break-even point for purchasing a bus pass at $33 per month or paying $1.50 per ride. This problem involves solving a linear equation to find how many rides make the total cost equal. Suitable for students in Grades 6-8.

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