Microscopes and Students: How Many are Needed?

[L²Cc]

Simple algebra question

Homework Statement

In a biology class of s students, there are m microscopes available. if the instructor assigns one micrope to each student, 6 more microscopes will be needed. If the instructor had twice as many microscopes available and assigned one microscope to each student, 6 microscopes would be left over. What is the value of s?

Homework Equations

The Attempt at a Solution

I solved for s by "guess + check". I tried expressing the word problem algebraically, but I can't seem to get it right. I get a negative instead of a positive value, so I find the absolute value and end up with the final results. Yet, I'm sure there is another way out.
Here are my equations:
sm=m-6
Hence, s= (-6/m)
Second equation,
2ms=m+6
Then I do substitution and get -18??!
Also, my equations don't really illustrate what is described above.

 

[arildno]

"In a biology class of s students, there are m microscopes available. if the instructor assigns one micrope to each student, 6 more microscopes will be needed."

How is s and m related here? What equation does this wordiness reduce to?

"If the instructor had twice as many microscopes available and assigned one microscope to each student, 6 microscopes would be left over."

And here? What is the equation?

 

[neutrino]

Why is there a product of s and m?

In the first case, there are six students more than the number of microscopes available, i.e. the difference between the number of students and microscopes is 6.

s - m = 6


Now, can you get the second equation?

 

[L²Cc]

equation for second situation: s=2m-6
Thank you!

 

[arildno]

Indeed!
So, start solving the system.

 

[+Minkie+]

just by looking does s=18

 

[arildno]

just by looking does s=18

Let OP manage something on his own, okay?

Besides, he has already "guessed&checked"

 

[L²Cc]

Besides, he has already "guessed&checked"

arildno, it's (I'm) a she, and I did solve the system! Thank you!

 

[arildno]

arildno, it's (I'm) a she, and I did solve the system! Thank you!

Dear me. With such a masculine user name, I would never have guessed that.

 

[L²Cc]

!