If `66 2/3 %` of 75% of one-eighth of a certain number is 179, then `33(1)/( 3) %` of three-fourth of that number is `:`

Options

A. 537
B. 859.2
C. 716
D. 787.6

Answer

To solve the problem step-by-step, we will follow the instructions given in the video transcript and break it down into clear steps.

### Step 1: Understand the Problem
We need to find a certain number \( x \) such that \( 66 \frac{2}{3} \% \) of \( 75\% \) of \( \frac{1}{8} \) of \( x \) equals 179.

### Step 2: Convert Percentages to Fractions
Convert \( 66 \frac{2}{3} \% \) to a fraction:
\[ 66 \frac{2}{3} \% = \frac{200}{3} \times \frac{1}{100} = \frac{2}{3} \]

Convert \( 75\% \) to a fraction:
\[ 75\% = \frac{75}{100} = \frac{3}{4} \]

### Step 3: Set Up the Equation
Now we can set up the equation based on the problem:
\[ \frac{2}{3} \times \frac{3}{4} \times \frac{1}{8} \times x = 179 \]

### Step 4: Simplify the Left Side
Simplify the left side of the equation:
\[ \frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{1}{2} \]
So, the equation becomes:
\[ \frac{1}{2} \times \frac{1}{8} \times x = 179 \]
\[ \frac{1}{16} \times x = 179 \]

### Step 5: Solve for \( x \)
To find \( x \), multiply both sides by 16:
\[ x = 179 \times 16 \]

### Step 6: Calculate \( 179 \times 16 \)
Now calculate \( 179 \times 16 \):
\[ 179 \times 16 = 2864 \]

### Step 7: Find \( 33 \frac{1}{3} \% \) of \( \frac{3}{4} \) of \( x \)
Next, we need to find \( 33 \frac{1}{3} \% \) of \( \frac{3}{4} \) of \( x \):
Convert \( 33 \frac{1}{3} \% \) to a fraction:
\[ 33 \frac{1}{3} \% = \frac{100}{3} \times \frac{1}{100} = \frac{1}{3} \]

Now set up the expression:
\[ \frac{1}{3} \times \frac{3}{4} \times x \]

### Step 8: Substitute \( x \) into the Expression
Substituting \( x = 2864 \):
\[ \frac{1}{3} \times \frac{3}{4} \times 2864 \]

### Step 9: Simplify the Expression
Simplifying:
\[ \frac{1}{3} \times \frac{3}{4} = \frac{1}{4} \]
So, we have:
\[ \frac{1}{4} \times 2864 \]

### Step 10: Calculate \( \frac{2864}{4} \)
Now calculate \( \frac{2864}{4} \):
\[ \frac{2864}{4} = 716 \]

### Final Answer
Thus, \( 33 \frac{1}{3} \% \) of \( \frac{3}{4} \) of the number is:
\[ \boxed{716} \]