To determine the unknown number, let's denote it as [tex]\( x \)[/tex].
The problem states that the number is as much greater than 31 as it is less than 75. This statement can be translated into the following equation:
[tex]\[ x - 31 = 75 - x \][/tex]
Here's a step-by-step solution:
1. Start with the equation:
[tex]\[ x - 31 = 75 - x \][/tex]
2. To solve for [tex]\( x \)[/tex], add [tex]\( x \)[/tex] to both sides of the equation to get rid of the [tex]\( x \)[/tex] on the right side:
[tex]\[ x + x - 31 = 75 \][/tex]
[tex]\[ 2x - 31 = 75 \][/tex]
3. Next, isolate [tex]\( 2x \)[/tex] by adding 31 to both sides of the equation:
[tex]\[ 2x - 31 + 31 = 75 + 31 \][/tex]
[tex]\[ 2x = 106 \][/tex]
4. Finally, solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{106}{2} \][/tex]
[tex]\[ x = 53 \][/tex]
Thus, the number that is as much greater than 31 as it is less than 75 is [tex]\( 53 \)[/tex].
The correct answer is:
(d) 53
