Step 1: Understanding the Concept:
Ratios represent the relative sizes of two or more values. In this case, a ratio of \(7:5\) for boys to girls tells us that for every \(7\) boys, there are exactly \(5\) girls.
The total strength of the class is composed of these two parts. To find absolute numbers, we must find the value of a single "part" or "unit" of the ratio.
The sum of the ratio parts (\(7 + 5 = 12\)) represents the entire class in terms of ratio units. By dividing the actual total headcount by the sum of ratios, we determine how many students equal one ratio part.
Step 2: Key Formula or Approach:
1. \(\text{Sum of Ratios} = \text{Ratio}_1 + \text{Ratio}_2\)
2. \(\text{Value of one part (x)} = \frac{\text{Total Quantity}}{\text{Sum of Ratios}}\)
3. \(\text{Number of Girls} = \text{Ratio of Girls} \times x\)
Step 3: Detailed Explanation:
Given:
Ratio of boys (\(B\)) to girls (\(G\)) = \(7 : 5\)
Total number of students = \(48\)
First, we find the total number of parts the class is divided into:
\[ \text{Total parts} = 7 + 5 = 12 \text{ units} \]
This means \(12\) units correspond to a total of \(48\) students.
Let's find the value of \(1\) unit:
\[ 1 \text{ unit} = \frac{48}{12} = 4 \text{ students} \]
Now that we know one unit represents \(4\) students, we can calculate the counts for each category.
The number of girls is represented by \(5\) units:
\[ \text{Number of girls} = 5 \times 4 = 20 \]
Similarly, if we wanted to find the number of boys:
\[ \text{Number of boys} = 7 \times 4 = 28 \]
Verification:
Adding boys and girls: \(28 + 20 = 48\). This matches the given total student count.
Ratio check: \(\frac{28}{20} = \frac{7}{5}\) (after dividing by \(4\)). This matches the given ratio.
Step 4: Final Answer:
The number of girls in the class is 20.