For brothers are splitting a sum of money between them. The first brother receive `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 many dollars are the four brothers splitting?

Options

A. `$50`
B. `$60`
C. `$75`
D. `$80`

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 brothers are splitting be represented as \( X \).

### Step 2: Calculate the shares of the first three brothers
- The first brother receives \( 50\% \) of \( X \), which is \( 0.5X \).
- The second brother receives \( 25\% \) of \( X \), which is \( 0.25X \).
- The third brother receives \( 20\% \) of \( X \), which is \( 0.2X \).

### Step 3: Sum the shares of the first three brothers
Now, we can add the shares of the first three brothers:
\[ 0.5X + 0.25X + 0.2X = 0.95X \]
This means that the first three brothers together receive \( 95\% \) of the total amount \( X \).

### Step 4: Determine the share of the fourth brother
Since the total percentage is \( 100\% \), the fourth brother receives the remaining amount:
\[ 100\% - 95\% = 5\% \]
Thus, the fourth brother receives \( 5\% \) of \( X \).

### Step 5: Set up the equation for the fourth brother's share
We know from the problem that the fourth brother receives \( \$4 \). Therefore, we can set up the equation:
\[ 5\% \text{ of } X = 4 \]
This can be written mathematically as:
\[ \frac{5}{100} \times X = 4 \]

### Step 6: Solve for \( X \)
To find \( X \), we can rearrange the equation:
\[ X = 4 \times \frac{100}{5} \]
Calculating this gives:
\[ X = 4 \times 20 = 80 \]

### Conclusion
The total amount of money that the four brothers are splitting is \( \$80 \).