When a number is increased by 24, It becomes 115% of itself. What is the number?

Options

A. 160
B. 250
C. 100
D. 200

Answer

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

### Step 1: Define the variable
Let the unknown number be represented by \( x \).

### Step 2: Set up the equation
According to the problem, when the number \( x \) is increased by 24, it becomes 115% of itself. We can express this mathematically as:
\[ x + 24 = 1.15x \]

### Step 3: Rearrange the equation
To isolate \( x \), we can rearrange the equation:
\[ x + 24 - 1.15x = 0 \]
This simplifies to:
\[ 24 = 1.15x - x \]
\[ 24 = 0.15x \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \) by dividing both sides of the equation by 0.15:
\[ x = \frac{24}{0.15} \]

### Step 5: Calculate \( x \)
Now, we perform the division:
\[ x = \frac{24}{0.15} = 160 \]

### Step 6: Conclusion
Thus, the number is \( 160 \).

### Verification
To verify, we can check if increasing \( 160 \) by \( 24 \) gives us \( 115\% \) of \( 160 \):
\[ 160 + 24 = 184 \]
Calculating \( 115\% \) of \( 160 \):
\[ 1.15 \times 160 = 184 \]
Both calculations match, confirming our solution is correct.