2100 `div`? `div` 84 = 1

Options

A. 28
B. 25
C. 24
D. 22

Answer

To solve the equation \( \frac{2100}{x} \div 84 = 1 \), we can follow these steps:

### Step 1: Rewrite the equation
The equation can be rewritten in a simpler form. We know that dividing by 84 is the same as multiplying by \( \frac{1}{84} \). Therefore, we can rewrite the equation as:
\[ \frac{2100}{x} \cdot \frac{1}{84} = 1 \]

### Step 2: Multiply both sides by 84
To eliminate the fraction, multiply both sides of the equation by 84:
\[ \frac{2100}{x} = 84 \]

### Step 3: Cross-multiply
Now, we can cross-multiply to solve for \( x \):
\[ 2100 = 84x \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides by 84:
\[ x = \frac{2100}{84} \]

### Step 5: Simplify the fraction
Now, we can simplify \( \frac{2100}{84} \):
1. First, find the greatest common divisor (GCD) of 2100 and 84.
2. The GCD is 12.
3. Now divide both the numerator and denominator by 12:
\[ x = \frac{2100 \div 12}{84 \div 12} = \frac{175}{7} = 25 \]

### Final Answer
Thus, the value of \( x \) is \( 25 \).

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