Four brothers splitting a sum of money between them. The first brother receives `50%` of the total, the second receive `25%` of the total, the third receives `20%` of the total, and the fourth receives the remaining `$4`. How much more does the first brother receive than the third brother?

Options

A. 4
B. 16
C. 20
D. 24

Answer

To solve the problem of how much more the first brother receives than the third brother, we can follow these steps:

### Step 1: Define the total amount of money
Let the total amount of money be denoted as \( x \).

### Step 2: Calculate the amounts received by each brother
- The first brother receives \( 50\% \) of the total, which is:
\[ \text{First brother's share} = 0.5x \]

- The second brother receives \( 25\% \) of the total, which is:
\[ \text{Second brother's share} = 0.25x \]

- The third brother receives \( 20\% \) of the total, which is:
\[ \text{Third brother's share} = 0.2x \]

- The fourth brother receives the remaining amount, which is given as \( 4 \).

### Step 3: Set up the equation for the fourth brother's share
Since the total amount \( x \) minus the shares of the first three brothers must equal the fourth brother's share, we can write:
\[ x - (0.5x + 0.25x + 0.2x) = 4 \]

### Step 4: Simplify the equation
Combine the terms inside the parentheses:
\[ 0.5x + 0.25x + 0.2x = 0.95x \]
Thus, the equation becomes:
\[ x - 0.95x = 4 \]
This simplifies to:
\[ 0.05x = 4 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by \( 0.05 \):
\[ x = \frac{4}{0.05} = 80 \]
So, the total amount of money is \( 80 \).

### Step 6: Calculate the amounts received by the first and third brothers
- The first brother receives:
\[ 0.5 \times 80 = 40 \]

- The third brother receives:
\[ 0.2 \times 80 = 16 \]

### Step 7: Find the difference between the amounts received
To find how much more the first brother receives than the third brother, subtract the third brother's amount from the first brother's amount:
\[ 40 - 16 = 24 \]

### Final Answer
The first brother receives \( 24 \) more than the third brother.

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