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Asked: 2023-11-06T10:23:07+00:00 In:

In a service. 1/4 of the people are men, 1/3 are women and the rest are children. If there are 50 children, how many a) people are there altogether? b) more women than men are there?

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In a service. 1/4 of the people are men,  1/3 are women and the rest are children.  If there are 50 children, how many

a) people are there altogether?

b) more women than men are there?

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  1. charles
    Begginer

    Given;

    Fraction of people that are men = \frac{1}{4}

    Fraction of people that are women = \frac{1}{3}

    Number of children = 50

    Let fraction of children be x

    When talking about fraction, a whole is = 1

    Sum of all the fractions should be equal to 1

    \frac{1}{4} + \frac{1}{3} + x = 1

    \frac{3+4}{12} + x = 1

    \frac{7}{12} + x = 1

    x = 1 - \frac{7}{12}

    x = \frac{12-7}{12}

    x = \frac{5}{12}

    \therefore the fraction of people that are children = \frac{5}{12}

    a) Let the number of people altogether be y

    Since the number of children was given, it is possible to find the number of people altogether.

    \frac{5}{12} of y = 50

    \frac{5}{12} \times y = 50

    \frac{5y}{12} = 50

    5y = 50 \times 12

    5y = 600

    y = \frac{600}{5}

    y = 120

    \therefore the number of people altogether is 120

    b) To find the number of more women than men, we need to find the number of men and women. After that, we subtract the number of men from the number of women.

    Number of men = \frac{1}{4} of 120

    = \frac{1}{4} \times 120

    = \frac{120}{4}

    = 30

    Number of women = \frac{1}{3} of 120

    = \frac{1}{3} \times 120

    = \frac{120}{3}

    = 40

    Number of more women than men = number of women – number of men

    = 40 - 30

    = 10

    \therefore the number of more women than men is 10.

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