The number of boys in a class is 36, and the ratio of boys and girls in the class is 2:3. Find the total number of students in the class.
Understand the Problem
The problem states that there are 36 boys in a class, and the ratio of boys to girls is 2:3. We need to find the total number of students in the class. This involves using the ratio to determine the number of girls and then adding that to the number of boys.
Answer
The total number of students is $36 + 54 = 90$.
Answer for screen readers
The total number of students in the class is 90.
Steps to Solve
- Set up the ratio
Let $b$ be the number of boys and $g$ be the number of girls. We are given the ratio of boys to girls is 2:3, so we can write this as: $$ \frac{b}{g} = \frac{2}{3} $$
- Substitute the number of boys
We know that $b = 36$, so we can substitute this into the equation: $$ \frac{36}{g} = \frac{2}{3} $$
- Solve for the number of girls
To solve for $g$, we can cross-multiply: $$ 36 \times 3 = 2 \times g $$ $$ 108 = 2g $$ Divide both sides by 2: $$ g = \frac{108}{2} = 54 $$ So, there are 54 girls.
- Calculate the total number of students
To find the total number of students, we add the number of boys and the number of girls: $$ \text{Total} = b + g = 36 + 54 = 90 $$
The total number of students in the class is 90.
More Information
The ratio 2:3 means that for every 2 boys, there are 3 girls. Since there are 36 boys, which is 18 times 2, then the number of girls will be 18 times 3. This gives us 54 girls.
Tips
A common mistake is to misinterpret the ratio or to calculate the number of girls incorrectly. Another error could be forgetting to add the number of boys and girls to find the total number of students.
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