Question

A local water park found that if the price of admission was $19, the attendance was about 1250 customers per day.When the price of admission was dropped to $11, attendance increased to about 2150 per day. Write a linearequation for the attendance in terms of the price,p. (A = mp + b)

Answer 1

$A\text{ = -112.5p + 3387.5}$Explanation:

when price of admission = $19

attendance = 1250 customers per day

The point (price, attendance) = (19, 1250)

when prcie of admission = $11

attendance = 2150 customers per day

The point (price, attendance) = (11, 2150)

Linear equation: A = mp + b

where m = slope

we use the two points (19, 1250) and (11, 2150) to get the slope:

$\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ x_1=19,y_1=1250,x_2=11,y_2\text{ = 2}150 \\ m\text{ = }\frac{2150\text{ - 1250}}{11\text{ - 19}} \\ m\text{ = }\frac{900}{-8} \\ m\text{ = slope = -112.50} \end{gathered}$$A\text{ = -112.5p + b}$

To get b, we will use any of the point and the slope:

$\begin{gathered} \text{using the point (11, 2150) = (p, A)} \\ A\text{ = -112.5p + b} \\ 2150\text{ = -112.5(11) + b} \\ 2150\text{ = -1237.5 + b} \\ 2150\text{ + 1237.5 = b} \\ b\text{ = 3387.5} \end{gathered}$$A\text{ = -112.5p + 3387.5}$