Step-by-step explanation:
If it takes Dan 32 minutes to complete two pages of homework, we can find out how many pages he completes in 200 minutes by setting up a proportion.
Let \(x\) be the number of pages he completes in 200 minutes.
The setup will be:
\(\frac{2 \text{ pages}}{32 \text{ minutes}} = \frac{x \text{ pages}}{200 \text{ minutes}}\)
Now, let's solve for \(x\):
\[x = \frac{2 \text{ pages} \times 200 \text{ minutes}}{32 \text{ minutes}}\]
\[x = \frac{400 \text{ pages}\cdot\text{minutes}}{32 \text{ minutes}}\]
\[x = 12.5 \text{ pages}\]
Therefore, at the same rate, Dan would complete approximately 12.5 pages of homework in 200 minutes.
