To solve this problem, we need to determine what number the given percentage represents.
We're given:
[tex]\[ 17 \frac{1}{3} + 21 \frac{1}{2} = 33 \frac{1}{3}\% \text{ of } ? \][/tex]
Let's break this down step-by-step:
1. Convert the mixed numbers to improper fractions or decimals:
[tex]\[
17 \frac{1}{3} = 17 + \frac{1}{3} \approx 17.3333
\][/tex]
[tex]\[
21 \frac{1}{2} = 21 + \frac{1}{2} = 21.5
\][/tex]
2. Add these two values together:
[tex]\[
17.3333 + 21.5 = 38.8333
\][/tex]
3. Convert the percentage [tex]\( 33 \frac{1}{3}\% \)[/tex] to a decimal:
[tex]\[
33 \frac{1}{3}\% = 33.3333\% = \frac{33.3333}{100} \approx 0.3333
\][/tex]
4. Set up the equation to find the unknown number [tex]\( x \)[/tex]:
[tex]\[
38.8333 = 0.3333 \times x
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{38.8333}{0.3333} \approx 116.5
\][/tex]
Therefore, the number that satisfies the equation is approximately [tex]\( 116.5 \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{116.5} \][/tex]
