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The ratio of the number of girls to the number of boys in a stamp club was 3 : 2 last year. When 15 boys joined the club this year, the ratio became 2 : 3. Find the total number of children in the club this year.

  • math -

    let the number of girls be 3x and the number of boys 2x
    (notice 3x : 2x = 3 : 2 )

    after the addition of boys
    number of girls = 3x
    number of boys = 2x + 15

    3x : 2x+15 = 2:3
    3x/(2x+15) = 2/3
    9x = 4x + 30
    5x = 30
    x = 6
    current number of girls = 18
    current number of boys = 27

    so number of children in the club now
    = 3x + 2x+15 = 5x + 15
    = 5(6) + 15 = 45

    check:
    original: girls = 18, boys = 12, notice ratio is 18:12 = 3:2
    after: girls = 18 , boys = 27 , notice 18:27 = 2:3
    and 18+27 = 45

    all is well.

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