20. a computer game lets you build your own amusement park. suppose
it costs you $25,000 a day to run the park. assume the average daily
attendance is 1250 people. how much should you charge for admission
if you want to make a profit of at least $30,000 for a 30-day month?
write an inequality to represent this situation, and solve.
ahhh idk how to write an equation ; -; pls

37500p - 750000 ≥ 30000 where p is the price of admission

Step-by-step explanation:

Lets work through it one bit at a time.

So, 25,000 a day to run it means every day you spend, or lose 25,000, so no matter what you will have - 25,000.

Using the daily average attendance , what if you charged 1 dollar per person, then each day you would make 1 dollar from each of the 1250 people, so each day you would make 1250 dollars.  if it were 2 dollars per person that's 2500 dollars from all the people.  let me know if you don't get that.

Now!  it says you want to change the ticket price, so let's call that p.  so now 1250p represents how much money you make.  of course you also have to subtract 25,000 from the first part so the EQUATION is 1250p - 25000.

Now, it wants an INEQUALITY to tell what price you should set to get 30,000 a month.  Well, for a 30 day month what does our equation look like?  30 days means you have 1250 people every day for 30 days, AND each day you lose 25000, so we multiply both by 30.  So now we have 37500p - 750000.  So now the equation tells us the profit for each 30 day month.

Finally we want the inequality to tell us the minimum amount to make at least 30,000 a month.  So in other words we want profit to be greater than or equal to 30,000

Profit ≥ 30000

37500p - 750000 ≥ 30000

Now you just use algebra to solve it.

37500p - 750000 ≥ 30000

37500p ≥ 780000

p ≥ 20.8

Which means admission for each person should be greater than or equal to $20.80.

Let me know if something was difficult to follow.  I also want to make a mention of something about inequalities, in case you didn't know.  If you ever have an inequality that looks like -5x < 15.  You would think you just divide both sides by -5.  With an inequality though, if you ever divide by a negative number you swap the direction fo the inequality sign.  so -5x < 15 becomes x > 3.  This took a while for me to memorize when I was learning so I always make a special point to mention it.

Anyway, I hope this makes sense.  Again, let me know if you need further help.  

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