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 25mpg in cities. Which of the following best approximates the number of city miles she drove in her car on this trip? Choose 1 answer: (A) 3.5 (B) 8.5 (C) 87.5 (D) 314.5

Calculate total mpg: Calculate the total miles per gallon (mpg) Sophia achieved on her trip. To find the overall mpg, divide the total miles driven by the total gallons of gas used. Total mpg = Total miles driven / Total gallons of gas used Total mpg = 402 miles / 12 gallons Total mpg = 33.5 mpgFind difference in mpg: Determine the difference in mpg between highway driving and city driving. The difference will help us understand how much each type of driving contributes to the overall mpg. Difference in mpg = Highway mpg - City mpg Difference in mpg = 37 mpg - 25 mpg Difference in mpg = 12 mpgCalculate weighted average: Calculate the weighted average to find out how many miles were driven in the city. Let x be the number of city miles and (402 - x) be the number of highway miles. We will set up an equation using the weighted average of the two mpg values. (25x + 37(402 - x)) / 402 = 33.5Solve equation for x: Solve the equation for x, the number of city miles. 25x + 14974 - 37x = 13467 -12x = -1507 x = 1507 / 12 x = 125.5833

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Math Problems

Algebra 1

Multi-step problems with unit conversions

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Q. During her last road trip, Sophia drove

402

miles on

12

gallons of gas. Sophia's car averages

37

miles per gallon

(\mathrm{mpg})

on highways and

25 \mathrm{mpg}

in cities. Which of the following best approximates the number of city miles she drove in her car on this trip?

\newline

Choose

1

answer:

\newline

(A)

3

5

\newline

(B)

8

5

\newline

(C)

87

5

\newline

(D)

314

5

Problem Understanding: Distance Sophia drove on total trip: $402 \text{ miles}$ $\newline$ Total gas for the trip: $12 \text{ gallons}$ $\newline$ Highway gas mileage = $37 \text{ mpg}$ $\newline$ City gas mileage = $25 \text{ mpg}$ $\newline$ Let $G$ = gallons used in city $\newline$ Then, $12 - G$ = gallons used in highway
Mileage formula: $\text{Gas mileage} = \frac{\text{Distance driven in miles}}{\text{Number of gallons of gas consumed}}$ $\newline$ Let $m = \text{gas mileage}$ , $d = \text{distance}$ , $g = \text{gallons of gas}$ . $\newline$ So the formula becomes $m = \frac{d}{g}$ $\newline$ Solve the mileage equation for distance: $\newline$ $d = mg$
Setting up the equation: We know that the total miles drove = $402$ $\newline$ Let, $x = \text{number of city miles}$ ; and $y = \text{number of highway miles}$ . $\newline$ So, $x + y = 402$ . $\newline$ Distance in City: $\newline$ $d=mg$ $\newline$ $x=25G$ $\newline$ Distance in Highway: $\newline$ $d=mg$ $\newline$ $y=37(12-G)$ $\newline$ Now, we have a system of 3 equations: $\newline$ $x + y = 402$ $\newline$ $x=25G$ $\newline$ $y=37(12-G)$
Solve for the value $G$ : Substitute the values of $x$ and $y$ in terms of $G$ in $x + y = 402$ . $\newline$ $25G + 37(12-G) = 402$ $\newline$ $25G + 444 - 37G = 402$ $\newline$ Combine like terms in left side: $\newline$ $444 - 12G = 402$ $\newline$ Subtract $444$ on both sides: $\newline$ $- 12G = -42$ $\newline$ Divide both sides by $-12$ to solve for $G$ . $\newline$ $G = \frac{-42}{-12}$ $\newline$ $G = \frac{7}{2} = 3.5$
Final Solution: Sophia used $3.5 \text{ gallons}$ in the city. $\newline$ $d=mg$ $\newline$ $d=25 \times 3.5$ $\newline$ $d=87.5$ $\newline$ Sophia drove $87.5 \text{ miles}$ in the city.