Answer:
-60.
Step-by-step explanation:
Let the unknown number be x.
Number is increased by 26 = x+26
Then result is tripled = 3(x+26)
Then the result is increased by 72 = 3(x+26)+72
Final result is [tex]\dfrac{1}{2}[/tex] of the number = [tex]\dfrac{1}{2}x[/tex]
[tex]3(x+26)+72=\dfrac{x}{2}[/tex]
[tex]3x+78+72=\dfrac{x}{2}[/tex]
[tex]3x+150=\dfrac{x}{2}[/tex]
Isolate variable terms.
[tex]3x-\dfrac{x}{2}=-150[/tex]
[tex]\dfrac{6x-x}{2}=-150[/tex]
Multiply both sides by 2.
[tex]5x=-300[/tex]
Divide both sides by 5.
[tex]x=-\dfrac{300}{5}[/tex]
[tex]x=-60[/tex]
Therefore, the required number is -60.
