0.75 of a number is 1200. 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 `5/8` of a number is, given that `0.75` of that number equals `1200`.

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

### Step 2: Set up the equation
According to the problem, we know that:
\[ 0.75 \times X = 1200 \]

### Step 3: Solve for \( X \)
To find \( X \), we can rearrange the equation:
\[ X = \frac{1200}{0.75} \]
To simplify this division, we can convert \( 0.75 \) to a fraction:
\[ 0.75 = \frac{75}{100} = \frac{3}{4} \]
Thus, we can rewrite the equation as:
\[ X = \frac{1200}{\frac{3}{4}} = 1200 \times \frac{4}{3} \]

### Step 4: Calculate \( X \)
Now we can perform the multiplication:
\[ X = 1200 \times \frac{4}{3} = 1200 \times 4 \div 3 = 4800 \div 3 = 1600 \]

### Step 5: Find \( \frac{5}{8} \) of \( X \)
Now that we have \( X = 1600 \), we need to find \( \frac{5}{8} \) of this number:
\[ \frac{5}{8} \times 1600 \]
Calculating this gives:
\[ \frac{5 \times 1600}{8} = \frac{8000}{8} = 1000 \]

### Final Answer
Thus, \( \frac{5}{8} \) of the number is \( 1000 \).

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