In the junior class of a certain school, there are 24 more girls than boys . If the ratio of girls to boys is 5:4. which is the number of girls in the junior class ?

Options

A. 216
B. 144
C. 120
D. 96

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define Variables
Let the number of boys in the junior class be \( x \). According to the problem, the number of girls will then be \( x + 24 \) (since there are 24 more girls than boys).

**Hint:** Start by defining your variables based on the information given in the problem.

### Step 2: Set Up the Ratio
We know the ratio of girls to boys is given as \( 5:4 \). This can be expressed mathematically as:
\[ \frac{\text{Number of Girls}}{\text{Number of Boys}} = \frac{5}{4} \]
Substituting the expressions for the number of girls and boys, we have:
\[ \frac{x + 24}{x} = \frac{5}{4} \]

**Hint:** Use the ratio given in the problem to create an equation involving your defined variables.

### Step 3: Cross Multiply
To eliminate the fraction, we can cross-multiply:
\[ 4(x + 24) = 5x \]

**Hint:** Cross-multiplication helps to simplify the equation by removing the fractions.

### Step 4: Expand and Rearrange
Expanding the left side gives:
\[ 4x + 96 = 5x \]
Now, rearranging the equation to isolate \( x \):
\[ 96 = 5x - 4x \]
This simplifies to:
\[ 96 = x \]

**Hint:** After expanding, collect like terms to isolate the variable on one side of the equation.

### Step 5: Find the Number of Girls
Now that we have \( x \), which is the number of boys, we can find the number of girls:
\[ \text{Number of Girls} = x + 24 = 96 + 24 = 120 \]

**Hint:** Substitute the value of \( x \) back into the expression for the number of girls to find the final answer.

### Conclusion
The number of girls in the junior class is \( 120 \).

**Final Answer:** 120