In a class of 50 students 34 are girls. What percent of the class are girls? What percent of the class are boys?
The Correct Answer and Explanation is:
Correct Answer:
- Percent of the class that are girls:
3450×100=68%\frac{34}{50} \times 100 = 68\%5034×100=68% - Percent of the class that are boys:
Total students = 50
Number of boys = 50 – 34 = 16
1650×100=32%\frac{16}{50} \times 100 = 32\%5016×100=32%
Textbook-Style Explanation (300 words):
To solve percentage problems involving a part and a whole, the formula used is:Percentage=(PartWhole)×100\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100Percentage=(WholePart)×100
In this case, the total number of students in the class is 50, and 34 of them are girls. This makes the girls the “part” and the class of 50 the “whole.” Substituting into the formula:Percentage of girls=(3450)×100=68%\text{Percentage of girls} = \left( \frac{34}{50} \right) \times 100 = 68\%Percentage of girls=(5034)×100=68%
This means that 68% of the class are girls.
To find the percentage of boys in the class, first calculate how many students are boys. Since there are 50 students total and 34 are girls:Number of boys=50−34=16\text{Number of boys} = 50 – 34 = 16Number of boys=50−34=16
Now, calculate what percent 16 is of 50:Percentage of boys=(1650)×100=32%\text{Percentage of boys} = \left( \frac{16}{50} \right) \times 100 = 32\%Percentage of boys=(5016)×100=32%
So, 32% of the class are boys.
Notice that the percentages of girls and boys add up to 100%:68%+32%=100%68\% + 32\% = 100\%68%+32%=100%
This confirms that the calculations are correct, as the total must always equal 100% in problems involving parts of a whole. This type of question is commonly seen in percentage and ratio topics in mathematics, and it helps learners understand how parts relate to a complete set.
