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There are only Chinese and Malay pupils in a hall.The ratio of the number of boys to the number of girls is 2:3.The ratio of the number of Chinese boys to the number of Malay boys is 5:3.There are 178 more Chinese boys than Malay boys.How many girls are there in the hall?

  • math -

    first step: express the clues algebraically:

    boys/girls = 2/3
    cboys/mboys = 5/3
    cboys = mboys+178

    Now, we want to find the number of girls. Just for ease of algebra, let's change the above to

    b/g = 2/3
    c/m = 5/3
    c = m+178

    3c = 5m
    3(m+178) = 5m
    2m = 534
    m = 267

    So, there are 267 Malay boys and 445 Chinese boys. That means b=712.

    Now, we know that 3b=2g, so

    g = 3/2 * 712 = 1068

    So, there are 1068 girls in the hall.

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