Hao and Mike shared a box of popcorn. If they ate all the popcorn in the box and Mike ate three times as much popcorn as Hao, what percent of the popcorn did Hao eat?

A. [tex]$20 \%$[/tex]
B. [tex]$25 \%$[/tex]
C. [tex]$30 \%$[/tex]
D. [tex]$33 \frac{1}{3} \%$[/tex]



Answer :

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].