Final answer:
To find the base number of which 15 1/3 is 26 2/3 percent, set up the equation 0.2667 * x = 46/3 and solve for x, giving the result of 57.5.
Step-by-step explanation:
The question asks us to find the base number of which 15 1/3 is 26 2/3 percent. To find this, we set up a proportion where 15 1/3 (which can also be written as 46/3 when converted to an improper fraction) is the part, 26 2/3% (or 26.67% when converted to a decimal, it is 0.2667) is the rate, and we are looking for the base (which we can call 'x').
We set up the equation as follows: 0.2667 * x = 46/3. To find x, we divide both sides by 0.2667, which yields x = (46/3) / 0.2667. After doing the division, we find that x = 57.5. Therefore, 15 1/3 is 26 2/3 percent of 57.5.
Understanding fractions, percentages, and how to find the whole from a percentage and a part are fundamental math skills necessary at this level, and this type of problem is common in high school mathematics. With practice, solving problems like this becomes more intuitive, and it's helpful to know the relationship between parts, whole, and percentages as illustrated by this example.