Question

Sylvia is organizing a small concert as a charity event at her school. She has done a little research and found the expression -10x + 180 represents the number of tickets that will sell at an event given that X represents the price of the ticket. Explain why the income of the event can be represented by the expression -10x^(squared) + 180x. If all the expenses add up to $150, explain why the expression -10x^ +180x-150 represents the profit. Please help. Thank you in advance and I can't make a number squares on this device so ^ is the symbol I used for squares

Answer 1

`\begin{gathered} \text{ the number of tickets }=-10x+180 \\ \text{ the price of a ticket }=x \end{gathered}`

The income of the event is given by the product of the number of tickets and the price of a ticket.

Hence, the income of the event can be represented by

`\text{ income of the event }=x(-10x+180)=-10x^2+180x`

The income of the event represented by -10x² + 180x

The profit is given by

`\text{ the profit }=(\text{ income of the event) - ( the expenses)}`

Therefore,

`\text{ the profit}=-10x^2+180x-150`

The profit is given by -10x² + 180x - 150