25% of a number is 258 less than the square of 25 What is the value of three-fourth of 43 percent of that number?

Options

A. 437.44
B. 477.33
C. 437.34
D. 473.43

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 number be \( x \).

### Step 2: Set up the equation
According to the problem, 25% of the number \( x \) is equal to the square of 25 minus 258. We can express this mathematically as:
\[ 0.25x = 25^2 - 258 \]

### Step 3: Calculate \( 25^2 \)
First, we calculate \( 25^2 \):
\[ 25^2 = 625 \]
Now substitute this value back into the equation:
\[ 0.25x = 625 - 258 \]

### Step 4: Simplify the right side
Now we simplify the right side:
\[ 625 - 258 = 367 \]
So we have:
\[ 0.25x = 367 \]

### Step 5: Solve for \( x \)
To find \( x \), multiply both sides of the equation by 4 (since \( 0.25 = \frac{1}{4} \)):
\[ x = 367 \times 4 \]
Calculating this gives:
\[ x = 1468 \]

### Step 6: Find 43% of \( x \)
Now we need to find 43% of \( x \):
\[ 43\% \text{ of } x = \frac{43}{100} \times 1468 \]
Calculating this gives:
\[ \frac{43}{100} \times 1468 = 631.24 \]

### Step 7: Find three-fourth of 43% of \( x \)
Now we need to find three-fourths of this value:
\[ \frac{3}{4} \times 631.24 \]
Calculating this gives:
\[ \frac{3}{4} \times 631.24 = 473.43 \]

### Final Answer
Thus, the value of three-fourth of 43 percent of that number is:
\[ \boxed{473.43} \]