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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

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) $314$ . $5$

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Multi-step problems with unit conversions

Full solution

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.

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