To determine the percentage of popcorn that Hao ate, let's proceed with a step-by-step solution:
1. Define Variables:
- Let [tex]\( H \)[/tex] represent the amount of popcorn Hao ate.
- Since Mike ate three times as much popcorn as Hao, let [tex]\( M = 3H \)[/tex] represent the amount Mike ate.
2. Total Amount of Popcorn:
- The total amount of popcorn [tex]\( T \)[/tex] is the sum of the amounts eaten by Hao and Mike.
- So, [tex]\( T = H + M \)[/tex].
3. Substitute Mike's Amount:
- Substituting [tex]\( M = 3H \)[/tex] into the total, we get [tex]\( T = H + 3H \)[/tex].
4. Simplify the Total:
- Simplifying the equation, [tex]\( T = 4H \)[/tex].
5. Calculate Hao's Percentage:
- The percentage of the popcorn Hao ate is given by the ratio of Hao's amount to the total amount, multiplied by 100.
- Thus, Hao's percentage is [tex]\( \left( \frac{H}{T} \right) \times 100 \)[/tex].
- Substituting [tex]\( T = 4H \)[/tex], we get [tex]\( \left( \frac{H}{4H} \right) \times 100 \)[/tex].
6. Simplify the Fraction:
- [tex]\( \frac{H}{4H} \)[/tex] simplifies to [tex]\( \frac{1}{4} \)[/tex].
7. Calculate the Percentage:
- Therefore, [tex]\( \left( \frac{1}{4} \right) \times 100 = 25\% \)[/tex].
So, the percentage of the popcorn that Hao ate is [tex]\( 25\% \)[/tex].
The correct answer is:
[tex]\( \boxed{25\%} \)[/tex].
