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21 November, 18:59

In psychology 101, the ratio of the number of girls to the number of boys is $3:1$. after one girl drops the class and three more boys sign up, the ratio of the number of girls to the number of boys becomes $5:2$. how many students are in the class after these changes?

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  1. 21 November, 19:20
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    Initially,

    g = number of girls;

    b = number of boys.

    Because the ratio of girls to boys is 3:1, therefore

    g = 3b (1)

    Finally, we have

    g-1 girls because one girl dropped the class;

    b+3 boys because three more boys signed up.

    Because the new ratio of girls to boys is 5:2, therefore

    (g - 1) / (b + 3) = 5/2

    Cross multiply.

    2 (g - 1) = 5 (b + 3)

    2g - 2 = 5b + 15

    2g - 5b = 17 (2)

    Substitute (1) into (2) to obtain

    2 (3b) - 5b = 17

    b = 17

    g = 3b = 3*17 = 51

    Final number of students in the class = 17 + 51 = 68

    Answer: 68
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