If 0.75 of a number is 1200, then what is `5/8` of that number?

Options

A. 1000
B. 1060
C. 880
D. 8002

Answer

To solve the problem step by step, we need to find out what \( \frac{5}{8} \) of a number is, given that \( 0.75 \) of that number equals \( 1200 \).

### Step 1: Set up the equation
Let the unknown number be \( x \). According to the problem, we have:
\[ 0.75 \times x = 1200 \]

### Step 2: Convert \( 0.75 \) to a fraction
We can express \( 0.75 \) as a fraction:
\[ 0.75 = \frac{75}{100} = \frac{3}{4} \]
So, we can rewrite the equation as:
\[ \frac{3}{4} \times x = 1200 \]

### Step 3: Solve for \( x \)
To isolate \( x \), we can multiply both sides of the equation by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \):
\[ x = 1200 \times \frac{4}{3} \]

### Step 4: Calculate \( x \)
Now, we perform the multiplication:
\[ x = 1200 \times \frac{4}{3} = \frac{1200 \times 4}{3} \]
Calculating \( 1200 \times 4 \):
\[ 1200 \times 4 = 4800 \]
Now divide by \( 3 \):
\[ x = \frac{4800}{3} = 1600 \]

### Step 5: Find \( \frac{5}{8} \) of \( x \)
Now that we have \( x = 1600 \), we need to find \( \frac{5}{8} \) of \( x \):
\[ \frac{5}{8} \times x = \frac{5}{8} \times 1600 \]

### Step 6: Calculate \( \frac{5}{8} \) of \( 1600 \)
To calculate this, we can first divide \( 1600 \) by \( 8 \):
\[ \frac{1600}{8} = 200 \]
Now multiply by \( 5 \):
\[ 5 \times 200 = 1000 \]

### Final Answer
Thus, \( \frac{5}{8} \) of the number is:
\[ \boxed{1000} \]