Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college $19,000. Assuming the college wishes to offer a total of 7 sections, to accommodate 220 students, and to bring in $278,000 in revenues, how many sections of each course should it offer?
Finite Math 1 section(s)
Applied Calculus 2 section(s)
Computer Methods 3 section(s)
To determine the number of sections the college should offer for each course, we need to set up a system of equations using the given information.
Let's assume the number of sections for Finite Math is x, for Applied Calculus is y, and for Computer Methods is z.
From the given information, we know the following:
1. Each section of Finite Math has 40 students, so the total number of students in Finite Math will be 40x.
2. Each section of Applied Calculus has 40 students, so the total number of students in Applied Calculus will be 40y.
3. Each section of Computer Methods has 10 students, so the total number of students in Computer Methods will be 10z.
Since the total number of sections should be 7, we have the equation:
x + y + z = 7 --(equation 1)
Also, the total number of students should be 220, so we have the equation:
40x + 40y + 10z = 220 --(equation 2)
Finally, the total revenue should be $278,000, so we have the equation:
40,000x + 60,000y + 19,000z = 278,000 --(equation 3)
Now, we need to solve this system of equations for x, y, and z.
One approach is to use substitution or elimination to solve the system of equations. However, since there are no fractions involved and the coefficients are relatively small, we can also solve it using an online matrix calculator or software like Microsoft Excel.
Using an online matrix calculator, you can input the coefficients of the variables and the constants of the equations (ignore the variables). After that, you can solve the system of equations by finding the matrix's inverse or using the "solve" function.
By solving this system of equations, we find:
x = 1 section(s) of Finite Math
y = 2 section(s) of Applied Calculus
z = 3 section(s) of Computer Methods
Therefore, the college should offer 1 section of Finite Math, 2 sections of Applied Calculus, and 3 sections of Computer Methods to accommodate 220 students and bring in $278,000 in revenues.