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Math Help - just checking

  1. #1
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    just checking

    The teacher gives the following homework assignment: You have to write an essay by tomorrow. You may work alone or in boy-girl pairs. As it turned out, 2/3 of the boys and 3/5 of the girls worked in pairs. What fraction of the class worked alone?

    3 and 5
    lcm=15

    3/5=9/15 2/3=10/15

    9/15-10/15=1/15

    I'm I doing the right thing
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  2. #2
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    Hello, mr.toronto!

    The teacher gives the following homework assignment: You have to write an essay.
    You may work alone or in boy-girl pairs.
    As it turned out, 2/3 of the boys and 3/5 of the girls worked in pairs.
    What fraction of the class worked alone?

    Let B = number of boys in the class.
    Let G = number of girls in the class.
    \. . Then there are A+B students in the class.

    2/3 of the boys worked in pairs: \frac{2}{3}B
    They paired off with 3/5 of the girls: \frac{3}{5}G
    . . Hence: . \frac{2}{3}B = \frac{3}{5}G\quad\Rightarrow\quad B = \frac{9}{10}G\;\;{\color{blue}[1]}


    Then 1/3 of the boys worked alone: . \frac{1}{3}B
    . . and 2/5 of the girls worked alone: . \frac{2}{5}G
    The fraction of students working alone is: . \frac{\frac{1}{3}B + \frac{2}{5}G}{B + G}\;\;{\color{blue}[2]}


    Substitute [1] into [2]: . \frac{\dfrac{1}{3}\left(\dfrac{9}{10}G\right) + \dfrac{2}{5}G}{\dfrac{9}{10}G + G} \;=\;\frac{\dfrac{7}{10}G}{\dfrac{19}{10}G} \;=\;\boxed{\frac{7}{19} }

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