Question

Zack plans to attend the Carroll County Fair and is trying to decide what would be a better deal. He can pay $40 for unlimited rides, or he can pay $15 for admission plus $1 per ride. If Zack goes on a certain number of rides, the two options wind up costing him the same amount. How many rides is that?Write a system of equations, graph them, and type the solution.

Answer 1

We have to express this problem as a system of equations.

The variables are cost "y" and the number of rides "x".

The first equation represents the cost for the unlimited rides.

The cost "y" is a constant value of $40 for any value of x, so it can be written as:

`y=40`

The second option correspond to a fixed cost of $15 and a variable cost of $1 per ride.

Then, we can write the cost as:

`y=15+1\cdot x=15+x`

If we want to graph the equations, we can see that the first equation is an horizontal line at $40.

The second equation is a line that has a y-intercept at y = 15 and a slope of 1.

We can graph them as:

The intersection seems to be at x = 25 rides.

We can check with the equations as:

`\begin{gathered} y=y \\ 40=15+x \\ x=40-15 \\ x=25 \end{gathered}`

Answer: the two options have the same cost for 25 rides.