It takes Dan 32 minutes to complete 2 pages of math homework. At this rate, many pages does he complete in 200 minutes?

To find out how many pages Dan completes in 200 minutes, we can use the concept of proportionality. Given: - Dan completes 2 pages in 32 minutes. We need to find: - How many pages Dan completes in 200 minutes. Let's denote the number of pages Dan completes in 200 minutes as \( x \). Since the rate of completing pages is constant, we can set up a proportion: \[ \frac{2 \text{ pages}}{32 \text{ minutes}} = \frac{x \text{ pages}}{200 \text{ minutes}} \] Now, we can solve for \( x \) to find out how many pages Dan completes in 200 minutes. Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{2}{32}=\frac{x}{200}\) - step1: Reduce the fraction: \(\frac{1}{16}=\frac{x}{200}\) - step2: Swap the sides: \(\frac{x}{200}=\frac{1}{16}\) - step3: Multiply both sides of the equation by \(200:\) \(\frac{x}{200}\times 200=\frac{1}{16}\times 200\) - step4: Multiply the terms: \(x=\frac{200}{16}\) - step5: Evaluate: \(x=\frac{25}{2}\) Therefore, Dan completes 12.5 pages in 200 minutes.