Help needed with a question (formula and solution)

[Mathsfatty]

Can someone help me with the formula and solution for the following question:

Q. "You are organising a meeting and the room costs $C to hire and you want to spend $F per person on food and drink. If the price per ticket is $P how many people need to come to break even?"

Thank you in advance for the help.

MF

 

[Deleted member 4993]

Can someone help me with the formula and solution for the following question:

Q. "You are organising a meeting and the room costs $C to hire and you want to spend $F per person on food and drink. If the price per ticket is $P how many people need to come to break even?"

Thank you in advance for the help.

MF

Please define "break even" for us - algebraically.

 

[Mathsfatty]

Please define "break even" for us - algebraically.

Thank you for responding. "Break even" in this case means that the total money paid out (price of meeting room and food and drink is the same as the money brought in by the total sale of tickets. So, no profit made and no loss. therefore total money paid out = total money recouped by tickets sold.

Doeas this help. I can't think of an algebraic way of putting it. Sorry.

MF

 

[Deleted member 4993]

Thank you for responding. "Break even" in this case means that the total money paid out (price of meeting room and food and drink is the same as the money brought in by the total sale of tickets. So, no profit made and no loss. therefore

total money paid out = total money recouped by tickets sold.

Doeas this help. I can't think of an algebraic way of putting it. Sorry.

MF

You got it.

Now,

If you sold "N" tickets what would be total money recouped by tickets sold.

and

How would you calculate - total money paid out

 

[Mathsfatty]

You got it.

Now,

If you sold "N" tickets what would be total money recouped by tickets sold.

and

How would you calculate - total money paid out

Would it be:

Money recouped = N x $P (where $P = price per ticket)

and Money out = $C + ($F x N) (where $C = cost of room and $F = cost food/drink per person)

This doesn't seem correct. It's a long long time since I've done any of this. And I loved (and still love) maths. I'm so embarraced that I can't remember it.

 

[Mathsfatty]

Would it be:

Money recouped = N x $P (where $P = price per ticket)

and Money out = $C + ($F x N) (where $C = cost of room and $F = cost food/drink per person)

This doesn't seem correct. It's a long long time since I've done any of this. And I loved (and still love) maths. I'm so embarraced that I can't remember it.

Is this anywahere near the correct formula? If it is, how do I go about solving for N?

 

[Deleted member 4993]

Money recouped = N x $P (where $P = price per ticket)

and Money out = $C + ($F x N) (where $C = cost of room and $F = cost food/drink per person)

That is the correct equation (remove those $ signs however).

so:

N * P = C + N * F

You want to solve for "N".

If you do not remember how to solve linear equation - for a quick review, go to this website:

http://www.purplemath.com/modules/solvelin3.htm

 

[Mathsfatty]

Money recouped = N x $P (where $P = price per ticket)

and Money out = $C + ($F x N) (where $C = cost of room and $F = cost food/drink per person)

That is the correct equation (remove those $ signs however).

so:

N * P = C + N * F

You want to solve for "N".

If you do not remember how to solve linear equation - for a quick review, go to this website:

http://www.purplemath.com/modules/solvelin3.htm

I think this is correct:

N=C/P-F

I hope this is OK? I have substituted values and it works out as long as P is always greater than F, which it would need to be in real terms in order to "break even".

If this is correct I would like to thank you very much for your time and help on this.

Kindest regards

MF

 

[Deleted member 4993]

I think this is correct:

N=C/P-F

I hope this is OK? I have substituted values and it works out as long as P is always greater than F, which it would need to be in real terms in order to "break even".

If this is correct I would like to thank you very much for your time and help on this.

Kindest regards

MF

I think you have done the problem correctly - but wrote it wrong!

The correct answer is:

\(\displaystyle N \ = \ \dfrac{C}{P-F}\)

or it can be written as:

N=C/(P-F)

what you wrote - traslates to:

\(\displaystyle N \ = \ \dfrac{C}{P} \ - \ F\) ...... and that is incorrect

 

[Mathsfatty]

I think you have done the problem correctly - but wrote it wrong!

The correct answer is:

\(\displaystyle N \ = \ \dfrac{C}{P-F}\)

or it can be written as:

N=C/(P-F)

what you wrote - traslates to:

\(\displaystyle N \ = \ \dfrac{C}{P} \ - \ F\) ...... and that is incorrect

Thank you. I had just written it wrong as I don't have the 'formula' option on my laptop.

Thank you very much for all of you help. It has been great. thank you again and have a lovely weekend.

MF

 

[Deleted member 4993]

Thank you. I had just written it wrong as I don't have the 'formula' option on my laptop.

Thank you very much for all of you help. It has been great. thank you again and have a lovely weekend.

MF

You have been a great student.

All you need to do is to use parentheses - like () - that grouping symbol signifies order of operation.