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Answer :
To solve this problem, we need to find the ratio of children to the total number of people at the playground. Here is the step-by-step solution:
1. Count the Children and Adults:
- There are 24 children at the playground.
- There are 16 adults at the playground.
2. Calculate the Total Number of People:
- Add the number of children and adults together:
[tex]\[
\text{Total people} = 24 \, (\text{children}) + 16 \, (\text{adults}) = 40
\][/tex]
3. Determine the Ratio of Children to Total People:
- The ratio of children to the total number of people is given by dividing the number of children by the total number of people. So, we simplify the expression 24 to 40 to find:
[tex]\[
\text{Ratio (children to total)} = \frac{24}{40}
\][/tex]
4. Find Equivalent Ratios:
- We simplify the ratio [tex]\(\frac{24}{40}\)[/tex] by finding common factors:
- The greatest common factor of 24 and 40 is 8.
- Divide both numbers by 8.
[tex]\[
\frac{24}{40} = \frac{24 \div 8}{40 \div 8} = \frac{3}{5}
\][/tex]
- Additionally, other equivalent ratios can be found by simplifying using different factors:
- Dividing both by 4 gives:
[tex]\[
\frac{24 \div 4}{40 \div 4} = \frac{6}{10}
\][/tex]
5. Choose the Equivalent Ratios:
- The equivalent ratios that represent the same relationship as the original ratio (children to total people) are: 24:40, 6:10, and 3:5.
Therefore, the three equivalent ratios that represent the relationship of children to total people are 24:40, 6:10, and 3:5.
1. Count the Children and Adults:
- There are 24 children at the playground.
- There are 16 adults at the playground.
2. Calculate the Total Number of People:
- Add the number of children and adults together:
[tex]\[
\text{Total people} = 24 \, (\text{children}) + 16 \, (\text{adults}) = 40
\][/tex]
3. Determine the Ratio of Children to Total People:
- The ratio of children to the total number of people is given by dividing the number of children by the total number of people. So, we simplify the expression 24 to 40 to find:
[tex]\[
\text{Ratio (children to total)} = \frac{24}{40}
\][/tex]
4. Find Equivalent Ratios:
- We simplify the ratio [tex]\(\frac{24}{40}\)[/tex] by finding common factors:
- The greatest common factor of 24 and 40 is 8.
- Divide both numbers by 8.
[tex]\[
\frac{24}{40} = \frac{24 \div 8}{40 \div 8} = \frac{3}{5}
\][/tex]
- Additionally, other equivalent ratios can be found by simplifying using different factors:
- Dividing both by 4 gives:
[tex]\[
\frac{24 \div 4}{40 \div 4} = \frac{6}{10}
\][/tex]
5. Choose the Equivalent Ratios:
- The equivalent ratios that represent the same relationship as the original ratio (children to total people) are: 24:40, 6:10, and 3:5.
Therefore, the three equivalent ratios that represent the relationship of children to total people are 24:40, 6:10, and 3:5.
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