Let the unknown number be [tex]\( x \)[/tex].
First, we are given that [tex]\( 75\% \)[/tex] of this number is added to 75. Converting [tex]\( 75\% \)[/tex] to a decimal, [tex]\( 75\% \)[/tex] is [tex]\( 0.75 \)[/tex] in decimal form. Therefore, [tex]\( 75\% \)[/tex] of the number [tex]\( x \)[/tex] is [tex]\( 0.75x \)[/tex].
According to the problem statement, when [tex]\( 0.75x \)[/tex] is added to 75, the result is equal to the number itself, [tex]\( x \)[/tex]. We can write this relationship as an equation:
[tex]\[ 0.75x + 75 = x \][/tex]
To isolate [tex]\( x \)[/tex], we need to get all terms involving [tex]\( x \)[/tex] on one side of the equation. Subtract [tex]\( 0.75x \)[/tex] from both sides:
[tex]\[ 75 = x - 0.75x \][/tex]
Combine like terms on the right side:
[tex]\[ 75 = 0.25x \][/tex]
Next, solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\( 0.25 \)[/tex]:
[tex]\[ x = \frac{75}{0.25} \][/tex]
Performing the division gives:
[tex]\[ x = 300 \][/tex]
Therefore, the unknown number is [tex]\( \boxed{300} \)[/tex].
