An experimental vehicle averages x miles per gallon when driven in the

This is identical to a question which asks for average speed. To find the answer we will use the equation: (Total Distance)/(Total Gallons Used) = 28

Total Distance: We are told that the car drives 120 miles in the city and 300 on the highway. \(120+300 = 420\)

Total Gallons Used: We know that in the city the car drives x miles per gallon. Therefore the total gallons of fuel used in the city will be \(\frac{120}{x}\)

We know on the highway that the car drives 2x miles per gallon. Therefore the total gallons of fuel used on the highway will be \(\frac{300}{2x}\)

Putting Together and Solving for x:

\(\frac{420}{\frac{120}{x}+\frac{300}{2x}}=28\)

\(\frac{420}{\frac{540}{2x}}=28\)

\(420 * \frac{2x}{540} = 28\)

\(x = 18\)

ANSWER C

Alternative method:

One could use alligation and the answer choices to very quickly find the answer:

One is essentially 'mixing' \(x\) and \(2x\) in a ratio of \(120:300\) (which simplifies to \(2:5\)) to get 28.

\(x\)                   \(2x\)
               
         \(28\)

\(2\)                       \(5\)        


Here we see that \(28 - x = 5\), rather than it being a simple numeric 5, it is a numeric value in a ratio which has been simplified. In other words, \(28 - x\) equals a multiple of 5. Which means \(x\) can be \(23\),\(18\) or \(13\) [I stopped here because the range of the answers is 14  to 28]. Only \(18\) can be found among the answer choices.

ANSWER C­

­
Total distance covered = 300+120 = 420 miles
Average mileage = 28 mpg------> Fuel consumed = 420/28 = 15 gallons

15 = 120/x + 300/2x ---------> x = 18
Option B

Can this also be solved using the teeter-totter method?

­An experimental vehicle averages x miles per gallon when driven in the city and 2x miles per gallon when driven on the highway. If the vehicle averages 28 miles per gallon when driven 120 miles in the city and 300 miles on the highway, what is the value of x?

\(\frac{120}{x} + \frac{300}{2x} = \frac{420}{28}\)

\(120 + 150 = \frac{420x}{28}\)

\(270 = 15x\)

\(18 = x\)

A. 14

B. 16

C. 18

D. 20

E. 28

Correct answer: C

­An experimental vehicle averages x miles per gallon when driven in the city and 2x miles per gallon when driven on the highway. If the vehicle averages 28 miles per gallon when driven 120 miles in the city and 300 miles on the highway, what is the value of x?

Alternative Approach

Use the answer choices.

We know that 28 is a weighted average of x and 2x. So, 28 has to be between x and 2x. Accordingly, we know the following.

x cannot be 14 since, in that case, 2x would be 28. So, 28 would not be between x and 2x.

Also, x cannot be 28 since, in that case there's no way for 28 to be between x and 2x.

A. 14

B. 16

C. 18

D. 20

E. 28

We're left with 16, 18 and 20.

28 is a weighted average of 120 * x and 300 * 2x. 300 is 2.5 times 120. So, 28 is weighted toward 2x.

16 is too low for x since 28 is pretty close to 32, rather than weighted a little over 2 times toward 32, which in that case would be 2x.

16

20 is to high because, if x were 20, 2x would be 40, and 28 is closer to 20 than 40. So, 28 is not weighted toward 40.

20

We're left with 18.

Correct answer: C