The ratio of the number of boys to the number of girls at a school is 11:9. There are 124 more boys than girls. Work out the total number of students at the school.
Answer (1)
Let the number of boys be 11 x and the number of girls be 9 x .
Set up the equation 11 x − 9 x = 124 to represent the difference between the number of boys and girls.
Solve for x : x = 62 .
Calculate the total number of students: 20 x = 20 × 62 = 1240 . The total number of students is 1240 .
Explanation
Problem Analysis Let's analyze the problem. We are given the ratio of boys to girls in a school and the difference between the number of boys and girls. We need to find the total number of students.
Setting up the Equation Let the number of boys be 11 x and the number of girls be 9 x . The difference between the number of boys and girls is given as 124. So, we can write the equation: 11 x − 9 x = 124
Solving for x Now, let's solve for x : 2 x = 124 Divide both sides by 2: x = 2 124 = 62
Finding the Number of Boys and Girls Now that we have the value of x , we can find the number of boys and girls: Number of boys = 11 x = 11 × 62 = 682 Number of girls = 9 x = 9 × 62 = 558
Calculating the Total Number of Students To find the total number of students, we add the number of boys and girls: Total number of students = 682 + 558 = 1240 Alternatively, we can calculate the total number of students as 20 x = 20 × 62 = 1240
Final Answer Therefore, the total number of students at the school is 1240.
Examples
Understanding ratios and differences is crucial in many real-world scenarios. For instance, if you're mixing ingredients for a recipe, knowing the ratio of flour to sugar helps you maintain the correct consistency and taste. Similarly, in business, understanding the ratio of assets to liabilities helps assess financial stability. This problem demonstrates how to use ratios and differences to find the total quantity, a skill applicable in various fields, from cooking to finance.
