Many of the following problems can be modeled with a linear equation. Analyze them and identify what quantities the variables x and y represent. The information provided in the problems is adequate to determine a point and a slope or two points on the line.
The manager of the Ivy Square Cinema observed that Friday night estimated ticket sales were 185 when the admission was $5. When the admission was increased to $6, the estimated attendance fell to 140.
(a) Use this information to find estimated attendance as a linear function of admission price.
(b) Use the function found in part (a) to estimate attendance if admission is increased to $7.
(c) Use the function found in part (a) to determine the admission price that will yield an estimated attendance of 250.
(d) The manager had no desire to set an admission price that would drive away all customers, but she was curious to know when that would occur. Based on the function in part (a), find the admission price that would result in a zero attendance. (Does this seem reasonable to you?)
(e) The manager was also curious to know what kind of attendance would result from free admission to all. (Popcorn sales should zoom upward.) Based on the function in part (a), find the estimated attendance for the manager. (Does this seem reasonable to you?)
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