Four brothers are splitting a sum of money between them. The first brother receives `50%` of the total, the second receives `25%` of the total, the third receives `20%` of the total, and the fourth receives the remaining `$4`. How may dollars are the four brothers splitting?

Options

A. `$60`
B. `$70`
C. `$80`
D. `$90`

Answer

To solve the problem of how much money the four brothers are splitting, we can follow these steps:

### Step 1: Define the total amount of money
Let the total amount of money that the four brothers are splitting be denoted as \( x \).

### Step 2: Calculate the shares of the first three brothers
- The first brother receives \( 50\% \) of the total amount:
\[ \text{First brother's share} = 0.5x \]

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

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

### Step 3: Calculate the total amount received by the first three brothers
Now, we can add the shares of the first three brothers:
\[ \text{Total received by first three brothers} = 0.5x + 0.25x + 0.2x \]

### Step 4: Simplify the total received by the first three brothers
Combining the terms:
\[ 0.5x + 0.25x + 0.2x = 0.95x \]

### Step 5: Set up the equation for the fourth brother
The fourth brother receives the remaining amount, which is given as \( 4 \) dollars. Therefore, we can set up the equation:
\[ x - 0.95x = 4 \]

### Step 6: Solve for \( x \)
This simplifies to:
\[ 0.05x = 4 \]
To find \( x \), divide both sides by \( 0.05 \):
\[ x = \frac{4}{0.05} \]

### Step 7: Calculate \( x \)
To remove the decimal, multiply by \( 100 \):
\[ x = 4 \times 100 = 400 \]

### Conclusion
Thus, the total amount of money that the four brothers are splitting is:
\[ \boxed{80} \]