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Math Help - ratio

  1. #1
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    ratio

    The ratio of boys to girls is 6:5 in one first-period class and 3:5 in a second first period class. If the school does not permit class sizes to be less than 10 students, what is the minimum number of total students in the two first-period classes so the ratio for the combined classes is 1:1?
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  2. #2
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    I stand corrected. Sorry for any confusion on my account.
    Last edited by Sirmio; January 30th 2010 at 05:02 PM. Reason: I was wrong.
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  3. #3
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    Hello, sri340!

    The ratio of boys to girls is 6:5 in Class #1, and 3:5 in Class #2.

    If the school does not permit class sizes to be less than 10 students,
    what is the minimum number of total students in the two classes
    so the ratio of boys to girls for the combined class is 1:1 ?
    Class #1 has: . 6a boys and 5a girls.
    Class #2 has: . 3b boys and 5b girls.

    We have this table: . \begin{array}{|c||c|c|} \hline<br />
& \text{Boys} & \text{Girls} \\ \hline \hline<br />
\text{Class 1} & 6a & 5a \\ \hline<br />
\text{Class 2} & 3b & 5b \\ \hline \hline<br />
\text{Total} & 6a+3b & 5a+5b  \\ \hline\end{array}


    We want: . (6a+3b):(5a+5b) \:=\:1:1 \quad\Rightarrow\quad 6a+3b \:=\:5a+5b \quad\Rightarrow\quad a \:=\:2b


    The table becomes: . \begin{array}{|c||c|c|} \hline<br />
& \text{Boys} & \text{Girls} \\ \hline \hline \text{Class 1} & 12b & 10b \\ \hline \text{Class 2} & 3b & 5b \\ \hline \hline \text{Total} & 15b & 15b \\ \hline\end{array}
    . . . . . . . . . . . . . . . . . . . . . . _{\uparrow\qquad \;\; \uparrow}
    . . . . . . . . . . . . . . . . . . . . . . . ^{\text{Check!}}


    If b = 1, Class #2 has only 8 students.


    Therefore: . b = 2\quad \begin{array}{|c||c|c|} \hline &\text{Boys} & \text{Girls} \\ \hline\hline \text{Class 1} & 24 & 20 \\ \hline \text{Class 2} & 6 & 10 \\ \hline \hline \text{Total} & 30 & 30 \\ \hline \end{array}


    The minimum number of students in the combined class is 60.

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