The equation [tex]$y=45 x$[/tex] represents the number of miles, [tex]$y$[/tex], Mr. Miller's car can travel using [tex]$x$[/tex] gallons of gas. Which data display represents a car that gets more miles per gallon than Mr. Miller's car?
A. Gas Mileage
| Number of Gallons | Number of Miles |
| :---------------- | :---------------- |
| 2 | 96 |
| 4 | 192 |
| 6 | 288 |
B. Gas Mileage
| Number of Gallons | Number of Miles |
| :---------------- | :---------------- |
| 5 | 195 |
| 10 | 390 |
| 15 | 585 |
C.
Answer (2)
Calculate the miles per gallon for each data display option.
Compare the calculated miles per gallon with Mr. Miller's car's mileage (45 mpg).
Identify the option(s) with a higher miles per gallon than Mr. Miller's car.
Select the correct option: A .
Explanation
Understanding the Problem Mr. Miller's car travels y = 45 x miles, where x is the number of gallons of gas. This means Mr. Miller's car gets 45 miles per gallon. We need to find which data display represents a car that gets more than 45 miles per gallon.
Calculating Miles Per Gallon for Each Option Let's calculate the miles per gallon for each option:
Option A: 2 gallons 96 miles = 48 miles per gallon 4 gallons 192 miles = 48 miles per gallon 6 gallons 288 miles = 48 miles per gallon
Option B: 5 gallons 195 miles = 39 miles per gallon 10 gallons 390 miles = 39 miles per gallon 15 gallons 585 miles = 39 miles per gallon
Option C: 10 gallons 455 miles = 45.5 miles per gallon
Comparing with Mr. Miller's Car Now, let's compare the miles per gallon for each option to Mr. Miller's car (45 mpg):
Option A: 48 mpg > 45 mpg Option B: 39 mpg < 45 mpg Option C: 45.5 mpg > 45 mpg
Both options A and C have a higher miles per gallon than Mr. Miller's car. However, since the question only allows one correct answer, and option A is the first one that satisfies the condition, we choose option A.
Final Answer Therefore, the data display that represents a car that gets more miles per gallon than Mr. Miller's car is option A.
Examples
Understanding miles per gallon is useful in everyday life when comparing the fuel efficiency of different cars. For example, if you are deciding between two cars, one that gets 30 miles per gallon and another that gets 40 miles per gallon, you can use this information to estimate how much you will spend on gas over a year. If you drive 12,000 miles per year, the first car will use 30 12000 = 400 gallons of gas, while the second car will use 40 12000 = 300 gallons of gas. If gas costs 3 p er g a ll o n , yo u w i ll s a v e (400 - 300) \times 3 = 300 per year by choosing the more fuel-efficient car.
Mr. Miller's car gets 45 miles per gallon. After calculating the miles per gallon for each option, Option A offers 48 mpg, which is higher than 45 mpg, making it the correct choice. Consequently, the answer is Option A.
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