Question

The Frederick County Fair costs $15.20 to get in and $2.50 per ride, while the Montgomery County Fair costs$10.00 to get in and $3.00 per ride.

Answer 1

`15.2+2.5x=10+3x`

Explanation:

This situation is represented by a linear function since it has an initial fee and a constant rate of change, linear functions are given as:

`\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{ constant rate of change (fee per ride)} \\ b=\text{ y-intercept} \end{gathered}`

Therefore, the equation for the two different situations:

`\begin{gathered} \text{ Frederick:} \\ y=15.2+2.5x \\ \text{ Montgomery:} \\ y=10+3x \end{gathered}`

Then, if we want to know where it would be equal, equalize the two equations:

`15.2+2.5x=10+3x`