`33 (1)/(3)%`of a number is 33. Find the number

Options

A. 9
B. 90
C. 99
D. `0.9`

Answer

To solve the problem, we need to find the number for which \( 33 \frac{1}{3}\% \) of it equals 33. Let's break down the steps:

### Step 1: Convert the mixed fraction percentage to a fraction
The percentage given is \( 33 \frac{1}{3}\% \). We can convert this mixed fraction into an improper fraction:
\[ 33 \frac{1}{3} = \frac{33 \times 3 + 1}{3} = \frac{99 + 1}{3} = \frac{100}{3} \]
So, \( 33 \frac{1}{3}\% = \frac{100}{3}\% \).

### Step 2: Convert percentage to a decimal
To convert the percentage to a decimal for calculations, we divide by 100:
\[ \frac{100}{3}\% = \frac{100}{3} \times \frac{1}{100} = \frac{1}{3} \]

### Step 3: Set up the equation
We know that \( \frac{1}{3} \) of the number \( x \) equals 33. Therefore, we can write the equation:
\[ \frac{1}{3} \times x = 33 \]

### Step 4: Solve for \( x \)
To find \( x \), we can multiply both sides of the equation by 3:
\[ x = 33 \times 3 \]

### Step 5: Calculate the value of \( x \)
Now, we calculate:
\[ x = 99 \]

### Conclusion
The number we are looking for is \( 99 \).

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