During her last road trip, Sophia drove 402 miles on 12 gallons of gas. Sophia's car averages 37 miles per gallon (mpg) on highways and 25 mpg in cities. Which of the following best approximates the number of city miles she drove in her car on this trip?

Question

During her last road trip, Sophia drove  402   miles on  12   gallons of gas. Sophia's car averages  37   miles per gallon  (mpg)  on highways and  25 mpg   in cities. Which of the following best approximates the number of city miles she drove in her car on this trip?

Bytelearn · Accepted Answer

Calculate average mpg: Calculate the total average miles per gallon (mpg) Sophia's car achieved on the trip. Sophia drove 402 miles on 12 gallons of gas. Average mpg for the trip = Total miles driven / Total gallons of gas used Average mpg for the trip = 402 miles / 12 gallons Average mpg for the trip = 33.5 mpgFind mpg difference: Determine the difference between the average mpg on highways and in cities. Difference in mpg = Highway mpg - City mpg Difference in mpg = 37 mpg - 25 mpg Difference in mpg = 12 mpgProportion of highway miles: Calculate the proportion of highway miles to city miles based on the average mpg. Since the average mpg for the trip (33.5 mpg) is closer to the highway mpg (37 mpg) than the city mpg (25 mpg), we can infer that Sophia drove more highway miles than city miles. However, we need to find a way to estimate the number of city miles.Set up equations: Set up a system of equations to represent the total miles driven. Let x be the number of highway miles and y be the number of city miles. We have two equations: x + y = 402 (total miles) (37x + 25y) / 12 = 33.5 (average mpg equation)Solve for city miles: Solve the system of equations for y (the number of city miles). First, we'll multiply the second equation by 12 to get rid of the fraction: 37x + 25y = 12 * 33.5 37x + 25y = 402 Now we have two equations with the same total miles: x + y = 402 37x + 25y = 402Identify mistake: Since we have two equations with the same total, we can set them equal to each other to find the relationship between x and y. 37x + 25y = x + y 36x = -24y x = -24y / 36 x = -2/3y This equation tells us that for every 3 miles driven in the city, Sophia drove -2 miles on the highway, which doesn't make sense. There is a mistake in the algebraic manipulation.

During her last road trip, Sophia drove $402$ miles on $12$ gallons of gas. Sophia's car averages $37$ miles per gallon (mpg) on highways and $25$ mpg in cities. Which of the following best approximates the number of city miles she drove in her car on this trip?

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During her last road trip, Sophia drove 402402402 miles on 121212 gallons of gas. Sophia's car averages 373737 miles per gallon (mpg) on highways and 252525 mpg in cities. Which of the following best approximates the number of city miles she drove in her car on this trip?

During her last road trip, Sophia drove $402$ miles on $12$ gallons of gas. Sophia's car averages $37$ miles per gallon (mpg) on highways and $25$ mpg in cities. Which of the following best approximates the number of city miles she drove in her car on this trip?