Question

Your soccer team is holding a silent auction dinner as a fundraiser to pay for school uniforms. The list shows all the expenses for the silent auction.

A tablet that costs $350
Football tickets that cost $150
A gift card that cost $125
The cost of the food is $500
The members of the soccer team will be selling tickets to the silent auction. A ticket to the silent auction includes chances to win prizes and dinner. The ticket cost is set so that 45 tickets will pay for the cost of the prizes and food.

Build a function that can be used to find the total profit, f(x), the soccer team earns by selling x tickets. Show your work to build this function.

Answer 1

Answer:69

Explanation:

A) $16

B) p(x) = 16x -800

C) 69 ticketsn:

A) The total of expenses is ...

$280 +100 +20 +400 = $800

If this is covered by 50 tickets, then a ticket must provide revenue of ...

$800/50 = $16

The cost per ticket is $16.

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B) The profit is the difference between revenue and expenses. The revenue from sale of x tickets will be 16x. The expenses are fixed at 800, so the profit is ...

p(x) = 16x -800

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C) We can find the number of tickets to sell (x) in order for profit to be at least $300 by solving the inequality ...

p(x) ≥ 300

16x -800 ≥ 300 . . . . . use the expression for p(x)

16x ≥ 1100 . . . . . . . . . add 800

x ≥ 68.75 . . . . . . . . . . divide by 16 . . . (the least satisfactory integer is 69)

In order to raise at least $300, the number of tickets sold must be at least 69.