Find the percentages. In a school containing 360 children, 198 are girls. The number of girls is what percent of the number of boys? The number of boys is what percent of the number of girls?
The Correct Answer and Explanation is:
Given:
- Total number of children = 360
- Number of girls = 198
- Therefore, number of boys = 360 – 198 = 162
Step 1: Find the percentage of girls compared to boys.
Percentage of girls compared to boys=(198162)×100=122.22%\text{Percentage of girls compared to boys} = \left( \frac{198}{162} \right) \times 100 = 122.22\%
Step 2: Find the percentage of boys compared to girls.
Percentage of boys compared to girls=(162198)×100=81.82%\text{Percentage of boys compared to girls} = \left( \frac{162}{198} \right) \times 100 = 81.82\%
Final Answers:
- Girls are 122.22% of the number of boys.
- Boys are 81.82% of the number of girls.
Explanation
Understanding percentages in relation to parts of a whole is an essential skill in real-life math. In this problem, we are asked to compare two groups—girls and boys—in terms of percentage. It’s important to note that we’re not just finding what percentage of the total each group is; we’re specifically comparing one group to the other.
We are told there are 360 children in a school, of whom 198 are girls. This means that the remaining students—360 minus 198—must be boys. So, there are 162 boys.
To find out what percent the number of girls is of the number of boys, we divide the number of girls by the number of boys and then multiply by 100. That is: (198÷162)×100=122.22%(198 ÷ 162) × 100 = 122.22\%
This result tells us that the number of girls is 122.22% of the number of boys, meaning there are more girls than boys.
Similarly, to find what percent the number of boys is of the number of girls, we divide the number of boys by the number of girls and multiply by 100: (162÷198)×100=81.82%(162 ÷ 198) × 100 = 81.82\%
This means the number of boys is 81.82% of the number of girls, again confirming that there are fewer boys than girls.
These calculations help us understand proportional relationships. Percentages over 100% indicate that one quantity is larger than the other, while percentages under 100% show that it’s smaller. This kind of comparison is useful in analyzing populations, budgets, or resources.
