To find out how many miles less Fabian's car travels on one gallon of gas than Alexandra's car, we first need to calculate the miles per gallon (mpg) for both Fabian's and Alexandra's cars.
For Fabian, the equation given is:
\[ y = 41.7x \]
To find out how many miles Fabian can travel on one gallon of gas, we'll substitute \( x = 1 \) into the equation:
\[ y = 41.7 \cdot 1 = 41.7 \text{ miles/gallon} \]
Now we need to determine the miles per gallon for Alexandra's car using the data provided in the table. We can calculate the miles per gallon for each row in the table by dividing the miles by the gallons for each entry.
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For \( x = 2 \) gallons, \( y = 86.4 \): \[ \text{mpg} = \frac{86.4}{2} = 43.2 \text{ miles/gallon} \]
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For \( x = 4 \) gallons, \( y = 172.8 \): \[ \text{mpg} = \frac{172.8}{4} = 43.2 \text{ miles/gallon} \]
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For \( x = 8 \) gallons, \( y = 345.6 \): \[ \text{mpg} = \frac{345.6}{8} = 43.2 \text{ miles/gallon} \]
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For \( x = 12 \) gallons, \( y = 518.4 \): \[ \text{mpg} = \frac{518.4}{12} = 43.2 \text{ miles/gallon} \]
From the calculations, we see that Alexandra’s car consistently achieves 43.2 miles per gallon across all data points.
Now, to find how many miles less Fabian's car travels on one gallon of gas than Alexandra's:
\[ \text{Difference} = \text{Alexandra's mpg} - \text{Fabian's mpg} \] \[ \text{Difference} = 43.2 - 41.7 = 1.5 \]
Thus, Fabian's car travels 1.5 miles less on one gallon of gas than Alexandra's car.
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