Story problem: company plans to send 224 employees to a conference and wants to....

[oregon789]

It seems like this problem should be easy, but I'm not sure if I should just be guessing numbers until I get what equals $12,000 or if there is a better mathematical way to solve it.

"a large company plans to send 224 employees to a conference and wants to put them up in a hotel. the hotel has 2-person rooms available for $120 and 3-person rooms available for $150. how many of each type of room should be reserved if the company wants to stay on budget with $12000?"

all I got so far is
120a+150b=12000
where a=# of 2-person rooms
and b=# of 3-person rooms

 

[ksdhart2]

So, to solve for two variables, you need two equations. You've found one, that's great. Now let's think about what we know, carefully re-read the problem text, and see if we can't come up with another. You're told that the number of employees staying at the hotel. Could that be important? Using your notation of having a 2-person rooms, how many people are saying in those rooms? And there are also b 3-person rooms, so how many people are staying in those rooms? What does that make the expression for the number of people at the hotel? How does that fit with the problem text that states that there are 224 employees staying at the hotel?

 

[Deleted member 4993]

It seems like this problem should be easy, but I'm not sure if I should just be guessing numbers until I get what equals $12,000 or if there is a better mathematical way to solve it.

"a large company plans to send 224 employees to a conference and wants to put them up in a hotel. the hotel has 2-person rooms available for $120 and 3-person rooms available for $150. how many of each type of room should be reserved if the company wants to stay on budget with $12000?"

all I got so far is
120a+150b=12000
where a=# of 2-person rooms
and b=# of 3-person rooms

Your first equation should be:

120 (a) + 150 * (b) ≤ 12000

and

2a + 3b = 224

Otherwise, you might get a non-integer solution for a & b.

 

[oregon789]

Your first equation should be:

120 (a) + 150 * (b) ≤ 12000

and

2a + 3b = 224

Otherwise, you might get a non-integer solution for a & b.

OK I understand that, but how do you solve it? I tried solving for one variable in the first equation and then subbing it into the second equation but I'm not getting answers that make sense.

 

[stapel]

OK I understand that, but how do you solve it? I tried solving for one variable in the first equation and then subbing it into the second equation but I'm not getting answers that make sense.

It is not possible to find errors in work that we cannot see. Please reply showing all of your efforts so far, starting from the set-up you were given. Thank you!