A boat operator wants to offer tours of San Francisco Bay. His profit P for a trip can be modeled by P(x) = −2x^2 + 120x − 788, where x is the cost per ticket. What range of ticket prices will generate a profit of at least $500?

14 to 46 tickets

Step-by-step explanation:

Step 1: Set up the equation

500 ≤ -2x² + 120x - 788

Step 2: Solve for x

0 ≤ -2x² + 120x - 1288

0 ≤ -2(x² - 60x + 644)

0 ≤ x² - 60x + 644

0 ≤ (x - 46)(x - 14)

14 ≤ x ≤ 46

Alternatively, we can graph the equation and determine the range by looking for where y = 500

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

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step-by-step explanation:

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