In a family the father took 1/4 of the cake and he had 3 times as much as others had the total number of family members is

Options

A. A)3
B. B)7
C. C)10
D. D)12

Answer

To solve the problem, let's break it down step by step.

### Step 1: Understand the problem
The father took 1/4 of the cake, and he had 3 times as much as each of the other family members combined. We need to find the total number of family members.

### Step 2: Define variables
Let:
- Total amount of cake = 1 unit
- Amount of cake taken by the father = 1/4 unit
- Amount of cake left for the other family members = 1 - 1/4 = 3/4 unit

### Step 3: Set up the equation
Let the number of other family members be \( n \). According to the problem, the father has 3 times as much cake as each of the other family members combined. Therefore, the amount of cake each of the other family members has can be represented as:

\[ \text{Amount each other member has} = \frac{3/4}{n} \]

### Step 4: Relate the father's share to the others' share
Since the father has 1/4 of the cake and this is equal to 3 times the amount each other member has, we can set up the equation:

\[ \frac{1}{4} = 3 \left( \frac{3/4}{n} \right) \]

### Step 5: Simplify the equation
Now, we can simplify the equation:

\[ \frac{1}{4} = \frac{9/4}{n} \]

### Step 6: Cross-multiply to solve for \( n \)
Cross-multiplying gives us:

\[ 1 \cdot n = 9 \implies n = 9 \]

### Step 7: Calculate total family members
Since \( n \) represents the number of other family members, we need to add the father to this count:

\[ \text{Total family members} = n + 1 = 9 + 1 = 10 \]

### Final Answer
The total number of family members is **10**.

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