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Math Help - Need help in forming equations for these two apparently simple scenarios!

  1. #1
    Rod
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    Need help in forming equations for these two apparently simple scenarios!

    No. 1
    Three eights of the class got sick. Three more students got sick, leaving only half the class at school. How many students were not sick?
    (possible choice of answer: 8, 12, 16, 20)

    No. 2
    3/4 of a jar of lollies are multi-coloured and the rest are black. 6 of the black lollies are eaten and now there is 6/7 of the jar of multicoloured lollies. How many black lollies were in the jar at the start?
    (possible answers: 6, 8, 10, 12)
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Rod View Post
    No. 1
    Three eights of the class got sick. Three more students got sick, leaving only half the class at school. How many students were not sick?
    (possible choice of answer: 8, 12, 16, 20)

    No. 2
    3/4 of a jar of lollies are multi-coloured and the rest are black. 6 of the black lollies are eaten and now there is 6/7 of the jar of multicoloured lollies. How many black lollies were in the jar at the start?
    (possible answers: 6, 8, 10, 12)
    Hi Rod,

    1. Let x = the total number of students

    \frac{3}{8}x = the number who initially got sick

    So, \frac{3}{8} of the total + 3 more = \frac{1}{2} the class (x).

    Equation: \frac{3}{8}x+3=\frac{1}{2}x

    Solve the equation to find the total number of students (x)

    x = 24

    \frac{3}{8}\left(24\right)=9 initially sick

    9+3=12 total sick students

    24-12=12 = number of students not sick.
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  3. #3
    MHF Contributor
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    Quote Originally Posted by Rod View Post
    No. 1: Three eights of the class got sick. Three more students got sick, leaving only half the class at school. How many students were not sick?
    What is the difference between one-half and three-eighths? (Hint: Subtract.)

    This fraction represents the three additional students. How many students were there, in total? (Hint: Since "1" means "one whole student body", figure out what you'd have to multiply by to convert the fraction from above into "1", and then multiply "3" by this value.)

    What is half of this number? (Hint: Divide by 2.)

    Quote Originally Posted by Rod View Post
    No. 2: 3/4 of a jar of lollies are multi-coloured and the rest are black. 6 of the black lollies are eaten and now there is 6/7 of the jar of multicoloured lollies. How many black lollies were in the jar at the start?
    This one works very much like the last one:

    If three-fourths were non-black, then one-fourth were black. If six-sevenths are now non-black, then one-seventh are now black.

    What is the difference between one-fourth and one-seventh?

    Since this fraction represents "six black", then what was the original number of black?

    If you get stuck, please reply showing how far you have gotten. Thank you!
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  4. #4
    Rod
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    Many thanks!

    Thanks for your help!
    In the land of the blind, the one eyed man is king, but he still only has one eye!
    Quote Originally Posted by masters View Post
    Hi Rod,

    1. Let x = the total number of students

    \frac{3}{8}x = the number who initially got sick

    So, \frac{3}{8} of the total + 3 more = \frac{1}{2} the class (x).

    Equation: \frac{3}{8}x+3=\frac{1}{2}x

    Solve the equation to find the total number of students (x)

    x = 24

    \frac{3}{8}\left(24\right)=9 initially sick

    9+3=12 total sick students

    24-12=12 = number of students not sick.
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  5. #5
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by Rod View Post
    No. 1
    Three eights of the class got sick. Three more students got sick, leaving only half the class at school. How many students were not sick?
    (possible choice of answer: 8, 12, 16, 20)

    No. 2
    3/4 of a jar of lollies are multi-coloured and the rest are black. 6 of the black lollies are eaten and now there is 6/7 of the jar of multicoloured lollies. How many black lollies were in the jar at the start?
    (possible answers: 6, 8, 10, 12)
    Lets say there are x students in class
    Initial case
    No. of students who are sick = 3x/8

    Second case
    No. of students sick = x/2

    According to question

    3x/8 + 3 = x/2

    ---solve it
    x = 24 , total no. of students healthy = x/2 = 12

    -------------------------------------
    Lets say initially x are there

    Initial case
    No. of colored = 3x/4
    So no. of black = x/4

    Second case
    No. of black = x/4 - 6

    No. of colored = 3x/4 (Unchanged)

    But total no. this time = x-6

    Hence Ratio is

    \frac{\frac{3x}{4}}{x-6} = \frac{6x}{7}

    ----
    \frac{3}{4x-24} = \frac{6}{7}

    21 = 24x - 144

    24x = 165

    x= a fraction take this appx. value to the closest number , in other words do round-off

    I hope I am not wrong
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  6. #6
    Rod
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    Can I rather solve by saying:
    let x = number of coloured lollies and y = number of blacks

    then the ratio 3/1 = x/y so x = 3y ........(1)

    and y-6 = 6/7x ............................................ .(2)

    substituting x = 3y in (2)

    DOESN'T WORK!
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