the management of a hotel found that they will sell all 800 tickets at 4 dollars per per person for a hour concert for one night only. For each 1 dollar increase in the gate fee, management expectes 100 fewer customers to buy tickets. How much should the management charge for gate fee so that it collects 3500 dollars from gate takings? hint. form equations and solve

Step-by-step explanation:

Let x represent the rate at which the ticket is sold and let y represent the number of tickets sold at that rate.

When x = 4, y = 800

This means that the income from gate takings at this rate is 4 * 800 = $3200

For each 1 dollar increase in the gate fee, management expects 100 fewer customers to buy tickets. It means that the amount earned would be (x + 1) (y - 100)

For the amount to be $3500, it means that

(x + 1) (800 - 100) = 3500

700 (x + 1) = 3500

x + 1 = 3500/700 = 5

Therefore, management should charge $5 per person for gate fee so that it collects 3500 dollars from gate takings.