If one-third of a number is 35, then what will be the 64% of that number?

Options

A. 67.2
B. 70.8
C. 61.4
D. 72.6

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Define the variable
Let the unknown number be represented as \( x \).

### Step 2: Set up the equation
According to the problem, one-third of the number is equal to 35. This can be expressed mathematically as:
\[ \frac{x}{3} = 35 \]

### Step 3: Solve for \( x \)
To find \( x \), we can multiply both sides of the equation by 3:
\[ x = 35 \times 3 \]
Calculating this gives:
\[ x = 105 \]

### Step 4: Calculate 64% of \( x \)
Now that we have found \( x \), we need to calculate 64% of this number:
\[ 64\% \text{ of } x = \frac{64}{100} \times x = \frac{64}{100} \times 105 \]

### Step 5: Simplify the calculation
We can simplify \( \frac{64}{100} \) to \( \frac{16}{25} \) (by dividing both the numerator and the denominator by 4):
\[ \frac{16}{25} \times 105 \]

### Step 6: Perform the multiplication
Now we can calculate:
\[ 16 \times 105 = 1680 \]
Now divide by 25:
\[ \frac{1680}{25} = 67.2 \]

### Final Answer
Thus, 64% of the number is:
\[ \boxed{67.2} \]