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A number is as much greater than 15 as it is less than 51. Find the number.
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].
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