Question

Katy’s favorite rides at the amusement park are the roller coaster and water slide. The wait time for the roller coaster is 30 minutes and the wait time for the water slide is 15 minutes. If she went on 20 rides total and waited 5 hours in line, how many times did she go on the roller coaster?

Answer 1

Let 'x' represent the number of times she went on the roller coaster

Let 'y' represent the number of times she went on the water slide.

If she went on 20 rides total,

The mathematical representation of the above statement is,

`x+y=20\ldots\ldots.1`

The wait time for the roller coaster is 30 minutes and the wait time for the water slide is 15 minutes. And we were told they waited for 5hours in line.

The mathematical representation of the above statement is,

`\begin{gathered} 30x+15y=5\text{hours}*60 \\ 30x+15y=300\ldots\ldots.2 \end{gathered}`

Combining the two equations together

`\begin{gathered} x+y=20\ldots\ldots.1 \\ 30x+15y=300\ldots\ldots.2 \end{gathered}`

Using substitution method, making 'x' the subject of formula in equation 1

`\begin{gathered} x+y=20 \\ x=20-y\ldots\ldots\text{.}.3 \end{gathered}`

Substitute x = 20 - y into equation 2 to solve for y

`\begin{gathered} 30(20-y)+15y=300 \\ 600-30y+15y=300 \\ -30y+15y=300-600 \\ -15y=-300 \\ (-15y)/(-15)=(-300)/(-15) \\ y=20 \end{gathered}`

Substitute y = 20 into equation 3 and solve for x

`\begin{gathered} x=20-y \\ x=20-20=0 \\ x=0 \end{gathered}`

Therefore, the number of times she went on the roller coaster is 0 time.

That means she did not ride on roller coaster at all.