The total number of students in a class is 65. If the total number of girls in class 35, then the ratio of the total number of boys to the number of girls is:

Options

A. a) `7:6`
B. b) `7 : 13`
C. c) `13 : 7`
D. d) `6 : 7`

Answer

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

### Step 1: Understand the total number of students
The total number of students in the class is given as 65.

### Step 2: Identify the number of girls
The total number of girls in the class is given as 35.

### Step 3: Calculate the number of boys
To find the number of boys, we can use the formula:
\[ \text{Total Students} = \text{Number of Boys} + \text{Number of Girls} \]
Let \( B \) be the number of boys. Therefore, we can write:
\[ B + 35 = 65 \]
Now, we can solve for \( B \):
\[ B = 65 - 35 \]
\[ B = 30 \]

### Step 4: Set up the ratio
Now that we have the number of boys (30) and the number of girls (35), we can set up the ratio of boys to girls:
\[ \text{Ratio of Boys to Girls} = \frac{B}{G} = \frac{30}{35} \]

### Step 5: Simplify the ratio
To simplify the ratio \( \frac{30}{35} \), we can divide both the numerator and the denominator by their greatest common divisor, which is 5:
\[ \frac{30 \div 5}{35 \div 5} = \frac{6}{7} \]

### Final Answer
The ratio of the total number of boys to the total number of girls is:
\[ 6 : 7 \]

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