College Algebra Linear Word Problem

Question

If full-time faculty are required to teach a minimum of 15 credits, is there anyway for a faculty member to teach a combination of 3-credit and 4-credit classes and teach exactly 15 credits? Write a linear equation that you could use to solve this problem. Make sure to define x and y. Solve the problem. (hint: there are 2 solutions).

Please help me figure this problem out! Thanks so much in advance!

Answer 1

Hello, thank you for taking the time to post your question!

The underlying equation that you want to solve here is

3x + 4y = 15 , where “x” represents the number of 3 credit hour courses and “y” represents the number of 4 credit hour courses

The two combinations that allow that to work are

x = 5, y = 0 … meaning 5 3-credit hour classes and 0 4-credit hour: 3(5) + 4(0) = 15

x = 1, y = 3 … meaning 1 3-credit hour class and 3 4-credit hour classes: 3(1) + 4(3) = 15

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

x=# of 3-credit courses

y=# of 4-credit courses

3x+4y=15

x=1

3+4y=15

4y=12

y=3

1 3-credit course and 3 4-credit courses is the only solution

the only other possibility is to teach 5 3-credit courses but then there are no 4-credit courses

if you are not limited to 15 credits, then you can teach 4 3-credit courses and 1 4-credit course for a total of 16 credits

there are other possibilities only if you are not limited to 15 credits