Select the correct answer. The owner of a live music venue is considering changing his entrance fee. He can model the projected profits based on price increases using this equation, where n is the number of $2 price increases. p(n) = -10n^2 + 50n + 7500 For which number of $2 price increases will he break even? A. 25 B. 2.5 C. 30 D. 25 and 30
Answers
Given : The owner of a live music venue is considering changing his entrance fee. He can model the projected profits based on price increases using this equation, where n is the number of $2 price increases. p(n) = -10n^2 + 50n + 7500
To Find : For which number of $2 price increases will he break even
Solution:
p(n) = -10n² + 50n + 7500
p(n)= 0 for break even
-10n² + 50n + 7500 = 0
=> n² - 5n - 750 = 0
=> n² - 30n + 25n - 750 =0
=> n(n - 30) + 25(n-30) = 0
=> (n + 25)(n-30) = 0
=> n = 30
30 is the answer
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Answer:
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