64 boys and 40 girls form a group for social work. During their membership drive, the same number of boys and girls joined the group. How many members does the group have now, if the ratio of boys to girls is 4:3 ?

Options

A. A) 168
B. B) 201
C. C) 147
D. D) 154

Answer

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

### Step 1: Define the variables
Let \( x \) be the number of boys and girls that joined the group during the membership drive.

### Step 2: Write the new counts of boys and girls
After the membership drive, the number of boys will be \( 64 + x \) and the number of girls will be \( 40 + x \).

### Step 3: Set up the ratio equation
According to the problem, the ratio of boys to girls after the membership drive is \( 4:3 \). We can express this as:
\[ \frac{64 + x}{40 + x} = \frac{4}{3} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 3(64 + x) = 4(40 + x) \]

### Step 5: Expand both sides
Expanding both sides results in:
\[ 192 + 3x = 160 + 4x \]

### Step 6: Rearrange the equation
Rearranging the equation to isolate \( x \):
\[ 192 - 160 = 4x - 3x \]
\[ 32 = x \]

### Step 7: Calculate the new number of boys and girls
Now that we have \( x = 32 \), we can find the new number of boys and girls:
- New number of boys = \( 64 + 32 = 96 \)
- New number of girls = \( 40 + 32 = 72 \)

### Step 8: Calculate the total number of members
The total number of members in the group now is:
\[ 96 + 72 = 168 \]

### Final Answer
The total number of members in the group now is **168**.

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