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Simplify the following ratios: 1) 14 boys to 21 girls, 2a) 80 standing to 128 seated, 2b) 128 seated to total audience (80+128)

Mathematics

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2 parts
a

5:8\text{5:8}

b

8:13\text{8:13}

3:2\text{3:2}

Step-by-step solution

10 steps

here are the solutions to your math homework problems, formatted as requested:

1. Ratio of boys to girls

Step 1: Identify the number of boys and girls.
Number of girls = 21
Number of boys = 14

Step 2: Write the ratio of boys to girls.
The ratio of boys to girls is 14:2114 : 21.

Step 3: Simplify the ratio by finding the greatest common divisor (GCD) of 14 and 21, which is 7. Divide both parts of the ratio by 7.

147:217=2:3\frac{14}{7} : \frac{21}{7} = 2 : 3

The ratio of boys to girls is 2:3\boxed{\text{2:3}}.

2. Theatre audience ratios

Part a· 3 steps

Ratio of standing audience to seated audience

  1. Identify the number of standing and seated audience members.

    Standing audience = 80
    Seated audience = 128

  2. Write the ratio of standing audience to seated audience.

    The ratio of standing to seated audience is $80 : 128$.

  3. Simplify the ratio by finding the GCD of 80 and 128, which is 16.

    Divide both parts of the ratio by 16.

    8016:12816=5:8\frac{80}{16} : \frac{128}{16} = 5 : 8

    The ratio of standing audience to seated audience is 5:8\boxed{\text{5:8}}.

Part b

8:13\text{8:13}

Ratio of seated audience to total number of audience

  1. Calculate the total number of audience members.

    Total audience = Standing audience + Seated audience
    Total audience = 80+128=20880 + 128 = 208

  2. Write the ratio of seated audience to total audience.

    The ratio of seated audience to total audience is $128 : 208$.

  3. Simplify the ratio by finding the GCD of 128 and 208, which is 16.

    Divide both parts of the ratio by 16.

    12816:20816=8:13\frac{128}{16} : \frac{208}{16} = 8 : 13

    The ratio of seated audience to total audience is 8:13\boxed{\text{8:13}}.

    3. Ratio of fine days to wet days in June

  4. Determine the total number of days in June and the number of wet days.

    Number of days in June = 30
    Number of wet days = 12

  5. Calculate the number of fine days.

    Number of fine days = Total days - Wet days
    Number of fine days = 30−12=1830 - 12 = 18

  6. Write the ratio of fine days to wet days.

    The ratio of fine days to wet days is $18 : 12$.

  7. Simplify the ratio by finding the GCD of 18 and 12, which is 6.

    Divide both parts of the ratio by 6.

    186:126=3:2\frac{18}{6} : \frac{12}{6} = 3 : 2

    The ratio of fine days to wet days is 3:2\boxed{\text{3:2}}.

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