Determining the Total Number of Students with a Given Ratio of Boys to Girls

Understanding how to calculate the total number of students when the ratio of boys to girls is given is a fundamental skill in basic arithmetic and algebra. This instructional guide examines the process using a variety of examples and step-by-step solutions. By the end of this article, readers will be able to apply these methods to other similar problems.

The Given Problem and its Solution

Let's consider the following problem: If there are 60 boys and 2000 girls, what is the total number of students?

Step-by-Step Solution:

Identify the ratio of boys to the total number of students. Let's call this ratio t. If 60 out of 2000 students are boys, then the ratio of boys is 60 / 2000 3 / 100.

Express this ratio as an equation: t * 100 / 40 2000.

Solving for t, we get: t 2000 * 40 / 100 800.

Therefore, the total number of students is 800.

Alternative Solutions and Explorations

Let's explore another way to solve this problem by considering the percentages and the total population.

Example 1: Solving for Total Number of Students

Let t be the total number of students. If 40% of the students are boys and 60% are girls, and we know there are 60 boys, we can set up the equation as follows:

40% of t 60 boys

0.40 * t 60

t 60 / 0.40 150

This would be incorrect, and we need to correct the approach as per the given problem.

For the correct approach, we can set up the equation:

60 boys 2000 girls 2060 students

This approach does not consider the 40% only for boys, but rather the given numbers directly.

Example 2: Using Ratios and Proportions

Another method involves using the given percentage directly, as demonstrated in the following examples:

We can set up the proportion as follows:

60 boys : 2000 girls 40 boys : x total students

Using cross-multiplication, we get:

6 2000 * 40

x 2000 * 40 / 60 1333.33

This is not a whole number, and it misinterprets the problem statement.

Correcting to the original problem:

40 boys : 2000 girls 40 boys : x total students

x 2000 students

Example 3: Using Algebraic Approach

Let's use algebra to solve for the total number of students:

Let t be the total number of students. Then:

40% of t number of boys

.40 * t 60

t 60 / .40 150

This solution is incorrect and does not match the given problem.

For the correct solution:

(60 boys 2000 girls) 2060 students

Total number of students 2060

By using these methods, we can see that the total number of students is 2060, considering the given boys and girls counts.

Conclusion

In summary, to find the total number of students when given the number of boys and girls, we need to set up the correct proportions and use the given data accurately. The total number of students is determined by adding the number of boys and girls together, which in this case is 2060. This method ensures that we accurately represent the given data and solve similar problems correctly.