To solve this problem, we will be using simultaneous equations.
Let's begin by establishing the equations required to solve this problem as displayed below:
Let no. of student rooms = x
Let no. of chaperone rooms = y
Equation No. 1 -
x + y = 27
Equation No. 2 -
120x + 90y = 2880
Now let's begin solving the simultaneous equations. First, we will make either ( x ) or ( y ) the subject in the first equation. In this example, we will be making ( x ) the subject as displayed below:
Equation No. 1 -
x + y = 27
x = 27 - y
We will now substitute the equation of ( x ) from the first equation into the second equation as displayed below:
Equation No. 2 -
120x + 90y = 2880
120 ( 27 - y ) + 90y = 2880
3240 - 120y + 90y = 2880
- 120y + 90y = 2880 - 3240
- 30y = - 360
y = - 360 / - 30
y = 12
After that, we will substitute the value of ( y ) from the second equation into the first equation to solve for ( x ) as displayed below:
Equation No. 1 -
x = 27 - y
x = 27 - ( 12 )
x = 15
Now, since we have calculated the amount of rooms which will be for students and faculty chaperones respectively, we now need to multiply the number of rooms by the number of students which will be in each room in order to achieve the total number of students as displayed below:
Total no. of students = No. of student rooms × No. students in each room = 15 × 4 = 60 students
Total no. of chaperones = No. of chaperone rooms × No. of chaperones in each room = 12 × 2 = 24 faculty chaperones
FINAL ANSWER:
Therefore, a total of 60 students and 24 faculty chaperones are on the trip.
