Question

Graham's car gets 25 miles per gallon in the city and 30 miles per gallon on the highway. Graham drives in the city and on the highway for 200 miles. He uses 7 gallons of gasoline. How many miles did he drive in the city?

А 25
B 50
С 75
D 100​

Answer 1

Explanation:

Let

Gallon in city = x

Gallon in highway = y

25x + 30y = 200 (i)

x + y = 7 (ii)

Multiplying ii by 30

30(x + y) = 30(7)

30x + 30y = 210 (iii)

On subtracting

30x + 30y - 25x - 30y = 210 - 200

5x = 10

x = 10/5

x = 2

Distance covered = 50

Answer 2

B

Explanation:

Let c represent the amount of gallons used in the city and h represent the amount of gallons used on the highway.

Graham drove a total of 200 miles. Since his car gets 25 miles per gallons in the city and 30 miles per gallon on the highway:

`\displaystyle 25c + 30 h = 200`

And he used a total of seven gallons. In other words:

`c + h = 7`

This yields a system of equations:

`\displaystyle \left\{ \begin{array}{l} 25c + 30h = 200 \\ c + h = 7\end{array}`

Since we want to determine the number of miles Graham drove in the city, we will solve for c using substitution. From the second equation, solve for h:

`\displaystyle h = 7 - c`

Substitute:

`\displaystyle 25 c + 30 ( 7 - c) = 200`

Solve for c:

`\displaystyle \begin{aligned} 25c + (210 - 30c) &= 200 \\ -5c &= -10 \\ c &= 2\end{aligned}`

Therefore, Graham used a total of two gallons in the city.

Since his car gets 25 miles per gallon in the city, Graham drove a total of:

`\displaystyle \frac{25 \text{ mi}}{\text{gal}} \cdot 2\text{ gal} = 50\text{ miles}`

Or 50 miles in the city.

In conclusion, our answer is B.