Let's break down the problem step by step.
1. Understanding the relationship between George and Pete's wealth:
Given that George is [tex]\( 33 \frac{1}{3} \% \)[/tex] richer than Pete, we can express George’s wealth in terms of Pete's wealth. Let's use a base number to make things simple. Suppose Pete's wealth is 100 units.
2. Calculating George's wealth:
If George is [tex]\( 33 \frac{1}{3} \% \)[/tex] richer than Pete, this means George has Pete's wealth plus [tex]\( 33 \frac{1}{3} \% \)[/tex] of Pete's wealth.
[tex]\[
\text{George's wealth} = 100 + 33.33 = 133.33 \text{ units}
\][/tex]
3. Finding Pete's percentage of George's wealth:
Now, we need to determine what percentage Pete’s wealth (100 units) is of George’s wealth (133.33 units).
[tex]\[
\text{Pete's percentage of George's wealth} = \left( \frac{100}{133.33} \right) \times 100
\][/tex]
4. Calculating Pete's percentage:
Performing the division, we get approximately:
[tex]\[
\left( \frac{100}{133.33} \right) \times 100 \approx 74.99\%
\][/tex]
5. Determining how much poorer Pete is:
To find the percentage by which Pete is poorer than George, we look at the difference between the whole (100%) and Pete's percentage of George’s wealth.
[tex]\[
\text{Percentage poorer} = 100\% - 74.99\% = 25\%
\][/tex]
Therefore, Pete is approximately [tex]\( 25 \% \)[/tex] poorer than George.
So, the correct answer is:
[tex]\[ \boxed{25\%} \][/tex]
