To solve this problem, we need to calculate the number of gallons Scott would use to drive 284 miles, based on the rate provided.

Step-by-Step Solution:

1. Determine the rate of miles per gallon: Scott drives 355 miles using 17 gallons of gas. The rate of miles per gallon is: $\text{Rate} = \frac{\text{Miles}}{\text{Gallons}} = \frac{355}{17} = 20.88 \, \text{miles per gallon}.$

2. Set up a proportion: To find how many gallons $x$ Scott needs to drive 284 miles, use the proportion: $\frac{355}{17} = \frac{284}{x}.$

3. Solve for $x$: Cross-multiply: $355x = 284 \times 17.$ Calculate: $355x = 4828.$ Divide both sides by 355: $x = \frac{4828}{355} \approx 13.6 \, \text{gallons}.$

Final Answer:

Scott would need approximately 13.6 gallons of gas to drive 284 miles.

Would you like more details about solving proportions, or have any other questions?

Related Questions:

1. How do you set up and solve proportions in other contexts?
2. What is the formula for converting rates to other units?
3. Can this approach work for varying rates of fuel efficiency?
4. How does rounding impact the accuracy of such calculations?
5. What would be the result if the rate was given in kilometers per liter?

Tip:

Always double-check calculations when using proportions by verifying units on both sides of the equation.