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  1. #1
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    help word problems

    A group of boys and girls took a test. Exactly 2/3 of the boys and exactly 3/4 of the girls passed the test. If an equal number of boys and girls passed the test, what fraction of the entire group passed? help would be appreciated, thanks.
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  2. #2
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    Talking answer

    2/3 = 8/12

    3/4 = 9/12


    12 boys and 12 girls for a total of 24 students

    8+9 = 17 students passed (8 boys and 9 girls)
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  3. #3
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    Hello, jarny!

    A group of boys and girls took a test.
    Exactly 2/3 of the boys and exactly 3/4 of the girls passed the test.
    If an equal number of boys and girls passed the test,
    what fraction of the entire group passed?

    Let . \begin{array}{cc} B = \text{number of boys} \\ G = \text{number of girls}\end{array}

    \frac{2}{3} of the boys passed: . \frac{2}{3}B boys passed.

    \frac{3}{4} of the girls passed: . \frac{3}{4}G girls passed.

    . . Hence, a total of \frac{2}{3}B + \frac{3}{4}G students passed.


    There was a total of B + G students.

    . . Hence, the fraction that passed is: . \frac{\frac{2}{3}B + \frac{3}{4}G}{B + G} [1]


    We are told that: . \frac{2}{3}B\,=\,\frac{3}{4}G [2]
    . . and hence: . 8B \,=\,9G\quad\Rightarrow\quad G\,=\,\frac{8}{9}B [3]


    Substitute [2] and [3] into [1]: . \frac{\frac{2}{3}B + \frac{2}{3}B}{B + \frac{8}{9}B} \;=\;\frac{\frac{4}{3}B}{\frac{17}{9}B} \;= \;\boxed{\frac{12}{17}}

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