Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil

Question

Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mileage varies from 16 to 24 miles per gallon, what is the difference between the most and least that the gasoline for a 480-mile trip will cost?

A. $ 5.12
B. $ 7.04
C. $11.52
D. $14.40
E. $52.80

A. $ 5.12
B. $ 7.04
C. $11.52
D. $14.40
E. $52.80

ENGRTOMBA2018 · Accepted Answer

Sure look below.

You are given that the per gallon cost of gasoline varies from 0.96-1.12 $. The question now wants you to find the MAXIMUM possible difference between the least amount of money spent on gasoline and the largest amount of money spent i.e. to calculate max. trip cost - min. trip cost.

Mileage is given to be 16 to 24 miles per gallon ---> thus to travel 480 miles you will need gasoline in the range 480/24 to 480/16 --> 20 to 30 gallons.

Thus, for these 20-30 gallons of gasoline, you will need money (divide this task into 2 parts, 1 for 30 gallons and 2nd one for 20 gallons).

Case 1: for 30 gallons ---> you will end up spending 30*0.96 to 30*1.12$ ---> 28.8$ to 33.6$

Case 2: for 20 gallons ---> you will end up spending 20*0.96 to 20*1.12$ ---> 19.2$ to 22.4$

Thus, the maximum cost of the 480 mile trip = 33.6 $ and minimum = 19.2$ ---> difference = 33.6-19.2 = 14.4$. D is thus the correct answer.

Hope this helps.

Nova12 · Answer

I think you have a typo there. Shouldn't it be a "480-mile trip" to match the solutions?

Because I got $3.36-$1.92=$1.44, which would be D for the 480 mile trip instead of a 48 mile trip

arjunperiyasamys · Answer

i think there is a typo. 
either the options have to be less by a decimal point or the trip should be 480 miles

Bunuel · Answer

Edited. Thank you.

Ekland · Answer

Any generous heart here to explain a solution to this math?
I'll greatly appreciate the needful.
We are here to learn.
The error has been corrected.
 Bunuel  is human.
can someone just give a solution cos I find that question a little confusing.
thanks in advance.

Ekland · Answer

Something told me not to click not just kudos but also the follow button.
my confidence just increases by one point.
Thanks.
*hugs*

vishnucool · Answer

maximum cost of the 480 mile trip = 33.6 $ 
minimum = 19.2$
difference = 33.6-19.2 = 14.4$

. D is answer.

amanvermagmat · Answer

When we are given  price  of gasoline in dollars/gallon and the  mileage  in miles per gallon, then the cost of a trip for 'n' miles would be 
(n miles) * (dollars/gallon)/(miles/gallon).. = n miles * dollars/gallon * gallon/miles

Notice that when you cancel all the units from numerator and denominator you are only left with dollars, which is our required unit of the cost.

So for a 480 mile trip,  cost would be = 480 * price/mileage

This equation will be MAX when numerator (price) is MAX and denominator (mileage) is MIN
Thus MAX cost = 480 * 1.12/16 = $ 33.6

This equation will be MIN when numerator (price) is MIN and denominator (mileage) is MAX
Thus MIN cost = 480 * 0.96/24 = $ 19.2

Required difference = 33.6 - 19.2 = $ 14.4

Hence  D answer

ScottTargetTestPrep · Answer

To determine the most expensive price for gas, we take the smallest (worst) mileage and the largest price. Thus, for the 480 miles, the most expensive the gas could be is:
 
480 x 1.12/16 = $33.60
 
For the least expensive, we’d take the largest (best) mileage and the smallest price:
 
480 x 0.96/24 = $19.20
 
Thus, the difference is 33.6 - 19.2 = $14.40
 
Answer: D

Sr1994 · Answer

Here, we have to find out the maximum and minimum values. 
We get the minimum value when we take  Less price and best mileage 
We get the maximum value when we take  High price and worst mileage

Minimum(Best mileage) = (0.96/24)*480 = 19.20
Maximum(Worst mileage) = (1.12/16)*480 = 33.60

Difference => Max - Min = 33.60-19.20 =  14.40 
 Answer : D

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Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil

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