Certainly! Let's go through the problem step by step.
1. Determine the Heights:
First, we need to establish a certain height for Yi Hao to work with percentage increases and decreases. Let's assume Yi Hao's height is 100 units.
2. Calculate Ali's Height:
Ali is 8% taller than Yi Hao. To find Ali’s height, we calculate:
[tex]\[
\text{Ali's height} = \text{Yi Hao's height} + 8\% \text{ of Yi Hao's height}
\][/tex]
Given Yi Hao's height is 100 units, we have:
[tex]\[
\text{Ali's height} = 100 + 0.08 \times 100 = 100 + 8 = 108 \text{ units}
\][/tex]
3. Calculate Vani's Height:
Vani is 10% shorter than Yi Hao. To find Vani’s height, we calculate:
[tex]\[
\text{Vani's height} = \text{Yi Hao's height} - 10\% \text{ of Yi Hao's height}
\][/tex]
Given Yi Hao's height is 100 units, we have:
[tex]\[
\text{Vani's height} = 100 - 0.10 \times 100 = 100 - 10 = 90 \text{ units}
\][/tex]
4. Express Ali's Height as a Percentage of Vani's Height:
To express Ali's height as a percentage of Vani's height, we use the formula:
[tex]\[
\text{Percentage} = \left(\frac{\text{Ali's height}}{\text{Vani's height}}\right) \times 100
\][/tex]
Substituting the values we have:
[tex]\[
\text{Percentage} = \left(\frac{108}{90}\right) \times 100 = \left(\frac{108}{90}\right) \times 100 = 1.2 \times 100 = 120\%
\][/tex]
Therefore, Ali's height is 120% of Vani's height.
