Detailed Solutions to Questions on Finding Ratios

Detailed solutions to the questions on finding ratio are presented.

  1. There are 3 triangles and 6 squares. Find the ratios:
    1. Triangles to squares
    2. Squares to total
    3. Triangles to total

    Solution

    1. Number of triangles = 3, number of squares = 6. \[ \dfrac{\text{triangles}}{\text{squares}} = \dfrac{3}{6} \] Simplify by dividing numerator and denominator by 3: \[ \dfrac{1}{2} \; \] or \[ \;1:2\].
    2. Total = \(3 + 6 = 9\). \[ \dfrac{\text{squares}}{\text{total}} = \dfrac{6}{9} \] Simplify: \[ \dfrac{2}{3} \; \] or \[ \;2:3\].
    3. \[ \dfrac{\text{triangles}}{\text{total}} = \dfrac{3}{9} \] Simplify: \[ \dfrac{1}{3} \; \] or \[ \;1:3\].
  2. There are 300 boys and 500 girls in a school. Find the ratios:
    1. Boys to total
    2. Girls to total
    3. Boys to girls

    Solution

    Total = \(300 + 500 = 800\).
    1. \[ \dfrac{\text{boys}}{\text{total}} = \dfrac{300}{800} \] Divide numerator and denominator by 100: \[ \dfrac{3}{8} \; \] or \[ \;3:8\].
    2. \[ \dfrac{\text{girls}}{\text{total}} = \dfrac{500}{800} \] Divide numerator and denominator by 100: \[ \dfrac{5}{8} \; \] or \[ \;5:8\].
    3. \[ \dfrac{\text{boys}}{\text{girls}} = \dfrac{300}{500} \] Divide numerator and denominator by 100: \[ \dfrac{3}{5} \; \] or \[ \;3:5\].
  3. There are 200 chairs and 150 tables. Find the ratios:
    1. Chairs to total
    2. Total to tables

    Solution

    Total = \(200 + 150 = 350\).
    1. \[ \dfrac{\text{chairs}}{\text{total}} = \dfrac{200}{350} \] Divide numerator and denominator by 50: \[ \dfrac{4}{7} \; \] or \[ \;4:7\].
    2. \[ \dfrac{\text{total}}{\text{tables}} = \dfrac{350}{150} \] Divide numerator and denominator by 50 \[ \dfrac{7}{3} \; \] or \[ \;7:3\].
  4. There are 25 teachers, and 500 students of which 300 are girls. Find the ratios:
    1. Total students to teachers
    2. Boys to teachers

    Solution

    1. \[ \dfrac{\text{students}}{\text{teachers}} = \dfrac{500}{25} \] Divide by 25: \[ \dfrac{20}{1} \; \] or \[ \;20:1\].
    2. Number of boys = \(500 - 300 = 200\). \[ \dfrac{\text{boys}}{\text{teachers}} = \dfrac{200}{25} \] Divide by 25: \[ \dfrac{8}{1} \; \] or \[ \;8:1\].
  5. City A has a population of 420,000 people and 200 general practitioners (GPs). City B has a population of 460,000 people and 230 general practitioners. Which city has a higher ratio of GPs to people?

    Solution

    1. City A: \[ \dfrac{420{,}000}{200} = \dfrac{2100}{1} \; \] or \[ \;2100:1\].
    2. City B: \[ \dfrac{460{,}000}{230} = \dfrac{2000}{1} \; \] or \[ \;2000:1\].
    Since \[2100:1 > 2000:1\], City A has a higher ratio of GPs to people.

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