If 40% of a number is 290, then what is the number which is 20% more than the initial number?

Options

A. 870
B. 725
C. 825
D. 680

Answer

To solve the problem step by step, we will first find the initial number based on the information given, and then calculate the number that is 20% more than this initial number.

### Step 1: Set up the equation
Let the unknown number be \( x \). According to the problem, 40% of this number is equal to 290. We can express this mathematically as:
\[ 0.4x = 290 \]

**Hint:** To find the original number, we need to isolate \( x \) in the equation.

### Step 2: Solve for \( x \)
To find \( x \), we will divide both sides of the equation by 0.4:
\[ x = \frac{290}{0.4} \]

**Hint:** Dividing by a decimal can be simplified by multiplying both the numerator and denominator by 10.

### Step 3: Calculate \( x \)
Now, we perform the division:
\[ x = \frac{2900}{4} = 725 \]

**Hint:** You can simplify the division by breaking it down into smaller steps if needed.

### Step 4: Find 20% more than \( x \)
Now that we have the initial number \( x = 725 \), we need to find a number that is 20% more than this. To find 20% of \( x \), we calculate:
\[ 20\% \text{ of } 725 = 0.2 \times 725 \]

**Hint:** Remember that 20% can be expressed as a decimal (0.2) for easier calculation.

### Step 5: Calculate 20% of \( x \)
Calculating 20% of 725:
\[ 0.2 \times 725 = 145 \]

**Hint:** You can multiply directly or break it down into smaller parts (e.g., \( 0.2 \times 700 + 0.2 \times 25 \)).

### Step 6: Add 20% to the original number
Now, we add this 20% to the original number \( x \):
\[ 725 + 145 = 870 \]

**Hint:** When adding, ensure you align the numbers properly to avoid mistakes.

### Conclusion
The number which is 20% more than the initial number is:
\[ \boxed{870} \]