Question

An amusement park charges $20 for an all-day pass and $10 for a pass after 5 P.M. On Wednesday the amusement park collected $1000 in pass sales. This situation can be modeled by the equation 1000 = 20x + 10y where x is the number of all-day passes sold and y is the number of passes sold after 5 P.M. a. Find the x-intercept of the graph of the equation. What does it represent? b. Find the y-intercept of the graph of the equation. What does it represent? c. Graph the equation using a scale of 10 on the x- and y-axes.

Answer 1

Input data

$20 for all day pass

$ 10 for pass after 5pm

Wednesday park = $1000

Equation

1000 = 20x + 10y

Procedure

a) Find the x-intercept

Intercept with x occurs when y = 0

`\begin{gathered} 1000=20x+10(0) \\ x=(1000)/(20) \\ x=50 \end{gathered}`

The intercept with the x-axis means that only all-day passes are sold.

b) Find the y-intercept

Intercept with y occurs when x = 0

`\begin{gathered} 1000=20(0)+10y \\ 1000=10y \\ y=(1000)/(10) \\ y=100 \end{gathered}`

The y-axis intercept means that only passes are sold after 5pm.

c) graph