Final answer:
The number that, increased by 33 1/3% itself, results in 72 is 54. This is found by solving the equation x + (1/3)x = 72, which simplifies to x = 54.
Step-by-step explanation:
To find the number which, when increased by 33 1/3% of itself, gives 72, we can set up an equation. Let's call the number we're looking for x. The phrase "increased by 33 1/3% of itself" means we add 33 1/3% (which is equivalent to 1/3) of x to x itself. So, our equation to solve is x + (1/3)x = 72.
First, combine like terms to find a common denominator, which gives us (4/3)x = 72. Then, to isolate x, we multiply both sides by the reciprocal of 4/3, which is 3/4. This gives us x = 72 * (3/4), which simplifies to x = 54.
Therefore, the original number is 54.