Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Question

Diane plans to attend the Harrison County Fair and is trying to decide what would be a better deal. She can pay $40 for unlimited rides, or she can pay $16 for admission plus $1 per ride. If Diane goes on a certain number of rides, the two options wind up costing her the same amount. How many rides is that? What is that cost?

If Diane goes on
rides, the two options will both cost $

Answer 1

Let \( x \) be the number of rides Diane goes on.

We can set up the following equations for the two options:

1. Cost of unlimited rides: \( C_1 = 40 \)
2. Cost of admission plus rides: \( C_2 = 16 + 1x \)

To find out when the costs are the same, we set \( C_1 \) equal to \( C_2 \):

\[ 40 = 16 + 1x \]

Now, we can solve for \( x \):

1. Subtract 16 from both sides:

\[ 40 - 16 = x \]

2. This simplifies to:

\[ 24 = x \]

So, Diane can go on 24 rides.

Next, we find out the cost for both options when she goes on 24 rides:

For the unlimited rides option:

\[ C_1 = 40 \]

For the admission plus rides option:

\[ C_2 = 16 + 1(24) = 16 + 24 = 40 \]

Therefore, both options cost the same.

To fill in the blanks:

If Diane goes on 24 rides, the two options will both cost $40.