Certainly! Let's solve this step-by-step:
1. Define the variable:
Let the number be [tex]\( x \)[/tex].
2. Set up the condition:
According to the problem, the number [tex]\( x \)[/tex] is as much greater than 15 as it is less than 51. This means the distance of the number [tex]\( x \)[/tex] from 15 is equal to the distance of the number [tex]\( x \)[/tex] from 51.
3. Express the distances mathematically:
- Distance from 15 is given by [tex]\( x - 15 \)[/tex].
- Distance from 51 is given by [tex]\( 51 - x \)[/tex].
4. Set up the equation:
Since the distances are equal, we can set up the equation:
[tex]\[
x - 15 = 51 - x
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
By combining like terms, we get:
[tex]\[
x + x = 51 + 15
\][/tex]
[tex]\[
2x = 66
\][/tex]
6. Divide both sides by 2:
[tex]\[
x = \frac{66}{2}
\][/tex]
7. Simplify:
[tex]\[
x = 33
\][/tex]
Therefore, the number that is as much greater than 15 as it is less than 51 is [tex]\(\boxed{33}\)[/tex].
