A school committee invited 135 students to the annual function. If the ratio of number of boys to the girls was 4:5, then find the number of boys and girls invited by the committee

Options

A. 70,65
B. 47,88
C. 30105
D. 60,75

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Ratio
The ratio of boys to girls is given as 4:5. This means that for every 4 boys, there are 5 girls.

### Step 2: Set Up Variables
Let the number of boys be represented as \(4x\) and the number of girls as \(5x\), where \(x\) is a common multiplier.

### Step 3: Write the Total Students Equation
According to the problem, the total number of students invited is 135. Therefore, we can write the equation:
\[ 4x + 5x = 135 \]

### Step 4: Combine Like Terms
Combine the terms on the left side of the equation:
\[ 9x = 135 \]

### Step 5: Solve for \(x\)
Now, divide both sides by 9 to find the value of \(x\):
\[ x = \frac{135}{9} = 15 \]

### Step 6: Calculate the Number of Boys
Now that we have the value of \(x\), we can find the number of boys:
\[ \text{Number of boys} = 4x = 4 \times 15 = 60 \]

### Step 7: Calculate the Number of Girls
Next, we calculate the number of girls:
\[ \text{Number of girls} = 5x = 5 \times 15 = 75 \]

### Step 8: Conclusion
Thus, the number of boys invited is 60 and the number of girls invited is 75.

### Final Answer:
- Number of Boys: 60
- Number of Girls: 75

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