Inequality question

Are you asking for the variable that we are solving for or the caterer snacks fee per person (2.25)
 
Flo Rida said:
Are you asking for the variable that we are solving for or the caterer snacks fee per person (2.25)
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You wrote: 3.25 ≤ (750/P)+(P*2.25) ≥ 2.75
The expression in the middle is the cost per person, right? We want this cost to be between 2.75 and 3.25. So the right way to set up the inequality is:
2.75 ≤ cost per person ≤ 3.25
Do you agree?

Now, what is the cost per person?
It consists of 2 parts: band and caterer.
Band cost is $750/P.
Caterer cost per person in your expression is P*2.25. Do you see that this is incorrect?
 
Just like 4*5 is the same as 5*4 we have p*2.25 is the same as 2.25p.

Math has grammar just like any language and it is grammatically correct to say/write 2.25p instead of p*2.25 but again they are both the same.
 
It clearly states what the cost person for the catering is and it does not depend on the number of people who attend the event. Seriously, just reread the problem and you'll see the answer.
 
2.75<(750+2.25p)/p<3.25 (multiply all terms by p)

2.75p<750+2.25p<3.25p (subtract 2.25p from all terms)

.5p<750<p (which shows p>750 and p<1500

750<p<1500 (So people can vary from 751 to 1499)

Note: I did not include 750 or 1500 people because the question stated ‘between’ which would imply the end points are not included.
 
Jomo said:
per person is between 2.75 and 3.25? I assume that you mean that per person is between $2.75 and $3.25. What does that mean exactly?
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Meaning the least expensive cost per person will be $2.75 and the most expensive will be $3.25, depending on how many people, p, attend.
 
Flo Rida said:
Meaning the least expensive cost per person will be $2.75 and the most expensive will be $3.25, depending on how many people, p, attend.
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Oh, so p is not per person! It is cost per person!. Now we still need to be clearer! p is the cost per person for what????
To be able to do these problems we must know exactly what the variables mean precisely!

Hold on, at the end you are saying that p is how many people attend. So which is it!
 
Flo Rida said:
p=cost per person to attend celebration
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No, p as stated in problem is the number of people. The price per person is the cost of the band divided by number of people and 2.25 per person for catering. The price per person can be expressed as (750/p) + 2.25 or (750+2.25p)/p
 
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