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

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New post 07 Feb 2016, 10:33
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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

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Re: Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil  [#permalink]

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New post 16 Feb 2016, 12:52
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Nez wrote:
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.


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.
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Re: Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil  [#permalink]

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New post 11 Feb 2016, 12:59
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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
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Re: Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil  [#permalink]

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New post 11 Feb 2016, 22:58
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i think there is a typo.
either the options have to be less by a decimal point or the trip should be 480 miles
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Re: Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil  [#permalink]

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New post 12 Feb 2016, 02:29
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Re: Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil  [#permalink]

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New post 16 Feb 2016, 12:40
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.
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Re: Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil  [#permalink]

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New post 16 Feb 2016, 13:04
1
Engr2012 wrote:
Nez wrote:
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.


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.


Something told me not to click not just kudos but also the follow button.
my confidence just increases by one point.
Thanks.
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Re: Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil  [#permalink]

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New post 16 Feb 2016, 13:27
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maximum cost of the 480 mile trip = 33.6 $
minimum = 19.2$
difference = 33.6-19.2 = 14.4$

. D is answer.
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Re: Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil  [#permalink]

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New post 01 Jun 2017, 23:27
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
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Re: Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil  [#permalink]

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New post 05 Jun 2017, 15:51
1
Bunuel wrote:
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


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
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Re: Gasoline varies in cost from $0.96 to $1.12 per gallon. If a car’s mil  [#permalink]

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