Question

Revenue from single-day ticket sales at a local amusement park can be modeled by the function y=-x2+11x+42 and revenue from season pass sales can be modeled by the function y=-5x+81, where x represents the number of months past January and y represents the total revenue in tens of thousands of dollars.

Algebraically, determine after how many months the revenue from single-day ticket sales will equal the revenue from season pass sales. (The first time it occurs)


How much revenue will they have earned at this point in time from single-ticket and season pass sales?



Lots of points!

Answer 1

• 3 months
• $660,000 each, or $1,320,000 total

Explanation:

(a) The revenue from sales will be equal when ...

-x^2 +11x +42 = -5x +81

0 = x^2 -16x +39

0 = (x -13)(x -3)

According to this model, sales will be even after 3 months and after 13 months. The first time it occurs is after 3 months.

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(b) Sales of each media at that point in time will be ...

y = -5x +81 = -5(3) +81 = 66 . . . . tens of thousands of dollars

$660,000 will be earned from sales of single-tickets and from season pass sales, for a total of $1,320,000.