a number is as much greater than 21 as it is less than 71. find the number.

Answer

To solve the problem step by step, let's define the unknown number as \( x \).

### Step 1: Set up the equation
According to the problem, the number \( x \) is as much greater than 21 as it is less than 71. This can be expressed mathematically as:
\[ x - 21 = 71 - x \]

### Step 2: Simplify the equation
Now, we will simplify the equation:
\[ x - 21 + x = 71 \]
This simplifies to:
\[ 2x - 21 = 71 \]

### Step 3: Solve for \( x \)
Next, we will isolate \( x \) by adding 21 to both sides:
\[ 2x = 71 + 21 \]
Calculating the right side gives:
\[ 2x = 92 \]
Now, divide both sides by 2:
\[ x = \frac{92}{2} \]
This results in:
\[ x = 46 \]

### Step 4: Conclusion
Thus, the number is:
\[ \boxed{46} \]

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