Question: Two friends, Serenity and Julia, had just bought their first cars. The equation $y = 35.2x$ represents the number of miles, $y$, that Serenity can drive her car for every $x$ gallons of gas. The graph below represents the number of miles, $y$, that Julia can drive her car for every $x$ gallons of gas.
Julia's Gas Mileage
Miles Driven
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y
x
$(10,189)$
$(20,378)$
Gallons of Gas
Use the dropdown menu and answer-blank below to form a true statement.
Answer
Attempt 1 out of 2
Serenity can travel ____ miles ____ than Julia on one gallon of gas.
1. **State the problem:** We want to compare how many miles Serenity and Julia can each drive on one gallon of gas.
2. **Serenity's mileage:** Given by the equation $$y = 35.2x$$, where $y$ is miles and $x$ is gallons. For one gallon, substitute $x=1$:
$$y = 35.2 \times 1 = 35.2$$ miles.
3. **Julia's mileage:** From the graph, two points are given: $(10,189)$ and $(20,378)$. We find Julia's mileage per gallon by calculating the slope of the line connecting these points:
$$\text{slope} = \frac{378 - 189}{20 - 10} = \frac{189}{10} = 18.9$$ miles per gallon.
4. **Compare mileages:** Serenity drives $35.2$ miles per gallon, Julia drives $18.9$ miles per gallon.
5. **Form a true statement:** Serenity can travel $35.2 - 18.9 = 16.3$ miles more than Julia on one gallon of gas.
**Final answer:** Serenity can travel **16.3 miles more** than Julia on one gallon of gas.