Question

could someone help me with this

A charity organization had a fundraiser where each ticket was sold for a fixed price. They had to sell a few tickets just to cover necessary production costs of $1,200. After selling 200 tickets, they had a net profit of $12,000.Let P represent the net profit (in dollars) when they have sold n tickets.
Complete the equation for the relationship between the net profit and number of tickets sold.

Answer 1

Hey there! Welcome to QuestionCove!

Answer 2

hi and thank you

Answer 3

We want to write an equation for the net profit

What is net profit?
So look at it like this: they sold a few tickets and got the $1200
Then they continued to sell tickets until they sold 200 tickets and so then they made a net profit of $12,000
This means in all 200 tickets made them 12,000 + 1,200

Answer 4

so in all they made $13200 right?

Answer 5

Yes

So total profit is how much money they made on tickets after covering their 1,2000 expenses

So how would we write that as a formula?

How much money do they made on tickets?
They sold 200 tickets and got a total of $13,200

Answer 6

so would it be P=200n+13,200?

Answer 7

Not quite, we're trying to make an equation that we can use for any number tickets, not just 200

Total profits = ticket sales - expenses

The expenses given is a constant, it's $1200

After a certain number of tickets, anything more ticket proceeds becomes profit

Answer 8

But first we need to calculate how much each ticket costs so that way we can have a variable in the equation to calculate that if we sell n tickets, we've made n*ticket price money

Answer 9

Do you understand what I'm saying?

Answer 10

yea i understand

Answer 11

Good, and in general

Profit = Total money - expenses

The expenses here are our necessary production costs (the $1200)

The total money made would be from our ticket sales
once we calculate how much a ticket costs, we can just multiply that by 'n' and find how much we'd make if we were able to sell 'n' tickets and then we can calculate the total profit after that

Answer 12

so 1 ticket costs 60$ and 60*200=12000

Answer 13

Remember, 12000 is the net profit. That's the money they get to keep after they pay the costs.

The total money they made was 13,200
(12000+1200)

Answer 14

So divide that by 200 to find the cost for a ticket

Answer 15

so the 1 ticket is $66 then

Answer 16

Bingo, can you now write out the equation?

Answer 17

but how would I put that in a formula

Answer 18

So let's go back a little to the beginning

net profit
this is money that is extra after you pay off whatever costs

So imagine you have a toy that you bought for $25
And you sell it to me for $30

Did you make $30?
Well yes, but you had paid 25 for it so that means you really only made a $5 profit

Do you follow so far?

Answer 19

wait would it be P=200n+66 or P=66n+13200

Answer 20

yes

Answer 21

How would you find the total money made?

The only way we're making money is by selling tickets
So each ticket we sell gives us $66
And so if we sell n tickets

Are we making 66n or 200n

Answer 22

200n because 1 ticket is $66 and they ended up with $12000 and only needed $1200 to pay it off. am i right?

Answer 23

total profit = (all the money we made) - (any costs we had)

Our costs are a constant in this question

Answer 24

Nope, it would actually be 66n

Answer 25

So if you bought 1 ticket you'd make $66

If you buy 2 tickets, that would be 66*2 or 122

And so on so to calculate how much

Cost of ticket * number of tickets = total money made

So 66n is one part of the equation

Answer 26

Did you understand that

Answer 27

so would the other part be how much they only needed to pay off?

Answer 28

yea i got that

Answer 29

Yep!

So
P = (total money made) - (how much they needed to pay off)

So plug in what you know and let me know what you get!

Answer 30

so P=13200n-1200
i only got one shot with this answer so i cant get it wrong

Answer 31

where'd you get 13200n from

Remember what we said about 66n
Each ticket costs $66 and so we multiply by the number of tickets sold to calculate how much money was made

Answer 32

Don't try any answer without going through me haha ;b

Answer 33

right sorry so P=66n-1200

Answer 34

alright i wont haha

Answer 35

Hit it on the nail!

Answer 36

Good job :)
Hopefully you were able to follow and if you get any similar questions, it'll be ez pz for you

Answer 37

so thats the right answer and i wont get it wrong

Answer 38

yessir

Answer 39

ok well thank you for ur help ur amazing at this

Answer 40

Of course! It was my pleasure :)

Answer 41

ok so what about this one
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. After 1 months, he weighed 140 kilograms. He gained weight at a rate of 5.5 kilograms per month.
Let y represent the sumo wrestler's weight (in kilograms) after x months.

Answer 42

Open a new post for this as this one's become pretty lengthy to scroll