Microscopes and Students: How Many are Needed?

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Homework Help Overview

The problem involves a scenario in a biology class where the relationship between the number of students and available microscopes is explored. The original poster presents a word problem that leads to the formulation of algebraic equations to determine the number of students.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss how to express the relationships between students and microscopes algebraically. Questions arise about the correct formulation of equations based on the problem's wording, with attempts to clarify the connections between the variables.

Discussion Status

Participants have made progress in identifying equations that represent the problem. There is a mix of attempts to solve the equations and some participants suggest that the original poster should continue working through the problem independently. The discussion reflects a collaborative effort to clarify the setup and relationships involved.

Contextual Notes

There is mention of the original poster's previous attempts at "guess and check," indicating a struggle with the algebraic formulation. The discussion also highlights the importance of accurately interpreting the problem's conditions to derive the correct equations.

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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.
 
Last edited:
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"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?
 
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?
 
equation for second situation: s=2m-6
Thank you!
 
Last edited:
Indeed!
So, start solving the system.
 
just by looking does s=18
 
+Minkie+ said:
just by looking does s=18

Let OP manage something on his own, okay?

Besides, he has already "guessed&checked"
 
arildno said:
Besides, he has already "guessed&checked"

arildno, it's (I'm) a she, and I did solve the system! Thank you!
 
L²Cc said:
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.
 
  • #10
:wink: !
 

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