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Math Question?

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#1
 Carl Senior Member Join Date: Jun 2008 Posts: 1,876 Feedback: (0) Math Question?

If you can answer this question telling me how you got it, I would greatly appreciate it.

Students at Jayson's school are planning a school trip to Vancouver. Jayson is working with the organizers. They have gathered the following information about costs.
- The price of airfare for each person is \$600
- The cost of the hotel room is \$60 per night per student and twice that per night per adult.

a) Five teachers travel to Vancouver and stay seven nights. How many students could travel to Vancouver and stay for seven nights for the same total cost?

#2
 Dollar Senior Member Join Date: Jun 2008 Posts: 1,909 Feedback: (0) Math Question?

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#3
 KungFu Senior Member Join Date: Jun 2008 Posts: 555 Feedback: (0) Math Question?

First find how much it costs the 5 adults: 5(600 + 120?7)=7200
So if x = number of students, x(600 + 60?7) = 7200
1020x = 7200

So divide 7200 by 1020 and round down.
#4
 news Senior Member Join Date: May 2008 Posts: 1,754 Feedback: (0) Math Question?

Since it costs \$60 per night per student and twice that per night per adult, it will cost one adult \$120 to stay one night. Since the adults will spend 7 nights in Vancouver, the cost for the hotel will be \$120 times 7 nights, which is equal to \$840, then, since there are 5 teachers coming, you times the cost of one night for one teacher (\$840) by the number of teachers (5), which is \$4200. So the total cost for the hotel alone will be \$4200. In addition, it will cost \$600 per adult to fly to Vancouver, so the cost for airfare will be \$600 times the number of teacher going, which is 5, so airfare will be \$3000. Once you add the airfare and the hotel costs together, you can find that the cost for the trip for the teachers is \$7200.
Now, since it costs a student is \$60 per night, and the trip is 7 days long, the hotel cost for one student for the entire trip will be \$420. However, the number of students remains unknown, so we will give it the variable 's', which means it will cost \$420 times 's' (or 420s) for 's' amount of students to stay at the hotel. Also it costs \$600 per student to fly to Vancouver, so, using the same variable 's' (since the number of students flying is the same as the number of student staying at the hotel), the cost of airfare for 's' amount of students is equal to \$600 time 's' (or 600s). Now we can ad the cost of the airfare for the students with the cost of the hotel since both have the same variable, which is \$1020s.
This means that the cost for the teachers (\$7200) is equal to the cost of the students (\$1020s), this looks like 1020s=7200.
Now we isolate for 's', meaning that both sides of the equal sign in divided by 1020, which means (since 1020 divided by 1020 is 1), s = 7200/1020, which is equal to s=7.06. Since you cannot have a 'bit' of a student, the .06 can be ignored, so ***7 students can come for the same cost as 5 teachers.***
#5
 news Senior Member Join Date: May 2008 Posts: 1,754 Feedback: (0) Math Question?

5 adults and 10 students

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