`33 (1)/(3)%` of 633 + 129 = `66(2)/(3)`% of ?

Answer

To solve the equation \( 33 \frac{1}{3}\% \) of 633 + 129 = \( 66 \frac{2}{3}\% \) of \( x \), we will follow these steps:

### Step 1: Convert the mixed percentages to improper fractions
Convert \( 33 \frac{1}{3}\% \) and \( 66 \frac{2}{3}\% \) into improper fractions.

\[ 33 \frac{1}{3}\% = \frac{100}{3}\% \]
\[ 66 \frac{2}{3}\% = \frac{200}{3}\% \]

### Step 2: Write the equation in terms of fractions
Now, we can rewrite the equation using the fractions:

\[ \frac{100}{3} \times \frac{1}{100} \times 633 + 129 = \frac{200}{3} \times \frac{1}{100} \times x \]

### Step 3: Simplify the left side
Calculate \( \frac{100}{3} \times \frac{1}{100} \times 633 \):

\[ \frac{100 \times 633}{3 \times 100} = \frac{633}{3} = 211 \]

Now add 129:

\[ 211 + 129 = 340 \]

### Step 4: Set up the equation
Now we have:

\[ 340 = \frac{200}{3} \times \frac{1}{100} \times x \]

### Step 5: Simplify the right side
This simplifies to:

\[ \frac{200x}{300} = \frac{2x}{3} \]

### Step 6: Set the equation equal to each other
Now we can set the left side equal to the right side:

\[ 340 = \frac{2x}{3} \]

### Step 7: Solve for \( x \)
To solve for \( x \), multiply both sides by 3:

\[ 1020 = 2x \]

Now divide by 2:

\[ x = \frac{1020}{2} = 510 \]

### Final Answer
Thus, the value of \( x \) is \( 510 \).

---