Word problem-forming the equation

[Guest]

I need help with this question, I don't really get the wording.

The symphony orchestra is holding a fundraising banquet in a hotel. The hotel charges $200 for the banquet hall, plus $60 per person. TIckets are $100 ech. How many tickets must be sold to raise more than $10 000?

I thought the equation would be like 100x+60x+200>10 000, but that didn't work out.
Can you help me with the equation plz?

Thanks,
Anna

 

[tkhunny]

I need help with this question, I don't really get the wording.

The symphony orchestra is holding a fundraising banquet in a hotel. The hotel charges $200 for the banquet hall, plus $60 per person. TIckets are $100 ech. How many tickets must be sold to raise more than $10 000?

I thought the equation would be like 100x+60x+200>10 000, but that didn't work out.

You are SOooooooooooooooooo close. The one thing you have to MAKE UP is that the hotel does NOT own the orchestra, otherwise, they wouldn't charge them for the use fo the hall.

If x = The number of folks at the banquet

$200 + $60*x is how much the hotel charges - Expenses
$100*x is how much the orchestra brings in - Gross Sales

Gross Sales LESS Expenses = The Amount Raised

$100*x - ($200 + $60*x) > $10,000

All you missed was the one minus sign.

Of course, in the real world, not everyone who buys a ticket actually shows up. They might make a little more! (Depending on how the hotel counts attendance.)

 

[Matt]

Hi Anna,

Let x be the number of tickets sold. Then the total cost is 200+60x and the money taken in from ticket sales is 100x. Thus the net profit P of the whole event is:

. . . .

We want the orchestra's profit to be more than 10,000 dollars, so we require:

. . . . 40x - 200 > 10000

which can be solved for x to obtain:

. . . . x > 255

Thus, the orchestra must sell at least 256 tickets in order to turn a profit of more than $10,000.

edit: fixed.

 

[Denis]

You need 10000 + 200 = $10200 to break even.

Each ticket nets you 100 - 60 = $40

10200 / 40 = 255 to break even.

So you need to sell 256 to start making more than $10000.