A number is 68% of the other number. If the sum of these two numbers is 84% of 500, what is the bigger number ?

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Variables
Let the bigger number be \( x \). According to the problem, the other number is 68% of \( x \). Therefore, we can express the other number as:
\[ \text{Other number} = 0.68x \]

### Step 2: Set Up the Equation
The sum of the two numbers is given to be 84% of 500. We can calculate 84% of 500:
\[ 84\% \text{ of } 500 = \frac{84}{100} \times 500 = 420 \]
Now, we can set up the equation for the sum of the two numbers:
\[ x + 0.68x = 420 \]

### Step 3: Combine Like Terms
Combine the terms on the left side of the equation:
\[ 1.68x = 420 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 1.68:
\[ x = \frac{420}{1.68} \]

### Step 5: Simplify the Division
To simplify \( \frac{420}{1.68} \), we can multiply both the numerator and the denominator by 100 to eliminate the decimal:
\[ x = \frac{42000}{168} \]
Now, we can simplify \( \frac{42000}{168} \):
- Divide both the numerator and the denominator by 4:
\[ x = \frac{10500}{42} \]
- Now divide both by 6:
\[ x = \frac{1750}{7} = 250 \]

### Conclusion
Thus, the bigger number \( x \) is:
\[ \boxed{250} \]