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Simple algebraic question

  1. Feb 22, 2007 #1
    Simple algebra question

    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations


    3. 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: Feb 22, 2007
  2. jcsd
  3. Feb 22, 2007 #2

    arildno

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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?
     
  4. Feb 22, 2007 #3
    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?
     
  5. Feb 22, 2007 #4
    equation for second situation: s=2m-6
    Thank you!
     
    Last edited: Feb 22, 2007
  6. Feb 22, 2007 #5

    arildno

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    Indeed!
    So, start solving the system.
     
  7. Feb 22, 2007 #6
    just by looking does s=18
     
  8. Feb 22, 2007 #7

    arildno

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    Let OP manage something on his own, okay?

    Besides, he has already "guessed&checked"
     
  9. Feb 22, 2007 #8
    arildno, it's (I'm) a she, and I did solve the system! Thank you!
     
  10. Feb 22, 2007 #9

    arildno

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    Dear me. With such a masculine user name, I would never have guessed that.
     
  11. Feb 22, 2007 #10
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