Sure, let's tackle this problem step-by-step.
1. Identify the Relationship:
- The number of miles driven by Cooper is directly proportional to the number of gallons he used.
2. Establish a Proportional Relationship:
- Since the relationship is proportional, we can use the ratio of miles per gallon (miles/gallon) to find out how many gallons he would need for a different number of miles.
3. Calculate Miles per Gallon:
Let's use the data point for 33 gallons and 663.3 miles:
[tex]\[
\text{Miles per gallon} = \frac{\text{Miles Driven}}{\text{Gallons Used}} = \frac{663.3 \text{ miles}}{33 \text{ gallons}}
\][/tex]
Upon calculating, we find that:
[tex]\[
\text{Miles per gallon} \approx 20.1
\][/tex]
4. Determine the Gallons Needed for the Target Distance:
- We know the target distance is 874.35 miles. Using our miles per gallon rate, we can find out how many gallons would be necessary.
[tex]\[
\text{Required gallons} = \frac{\text{Target miles}}{\text{Miles per gallon}} = \frac{874.35 \text{ miles}}{20.1 \text{ miles per gallon}}
\][/tex]
Upon calculating, we find that:
[tex]\[
\text{Required gallons} \approx 43.5
\][/tex]
Conclusion:
To travel 874.35 miles, Cooper would need approximately 43.5 gallons of gas.
