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The city of Cortisville has two gas stations, Petrocort and Cortoline.

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The city of Cortisville has two gas stations, Petrocort and Cortoline.  [#permalink]

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New post 22 Feb 2017, 01:35
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Question Stats:

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The city of Cortisville has two gas stations, Petrocort and Cortoline. On a particular day, gasoline at Petrocort was sold for $2.78 per gallon and gasoline at Cortoline was sold for $3.28. If the average price per gallon for gasoline for the entire city that day was $2.99, what percent of all gasoline sold was sold at Cortoline?

A. 42%
B. 43%
C. 44%
D. 46%
E. 47%
Spoiler: OA

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Re: The city of Cortisville has two gas stations, Petrocort and Cortoline.  [#permalink]

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New post 22 Feb 2017, 01:45
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Bunuel wrote:
The city of Cortisville has two gas stations, Petrocort and Cortoline. On a particular day, gasoline at Petrocort was sold for $2.78 per gallon and gasoline at Cortoline was sold for $3.28. If the average price per gallon for gasoline for the entire city that day was $2.99, what percent of all gasoline sold was sold at Cortoline?

A. 42%
B. 43%
C. 44%
D. 46%
E. 47%


Weighted Average Method:

2.78P + 3.28C = 2.99(P+C)

i.e. 0.21P = 0.29C
i.e. P/C = 29/21

C as a % of total Gasoline = [21/(21+29)]*100 = 42%

Answer: Option A
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Re: The city of Cortisville has two gas stations, Petrocort and Cortoline.  [#permalink]

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New post 22 Feb 2017, 06:38
Answer : A

2.78P + 3.28C = 2.99(P+C)

P____________________C
2.78_______________3.28
_________2.99
0.29_______________0.21

Therefore, 0.21P = 0.29C
or C/P = 21/29

C/(C+P) % = [ 21 / (21+29) ] * 100 % = 42%
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Re: The city of Cortisville has two gas stations, Petrocort and Cortoline.  [#permalink]

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New post 22 Feb 2017, 10:41
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Bunuel wrote:
The city of Cortisville has two gas stations, Petrocort and Cortoline. On a particular day, gasoline at Petrocort was sold for $2.78 per gallon and gasoline at Cortoline was sold for $3.28. If the average price per gallon for gasoline for the entire city that day was $2.99, what percent of all gasoline sold was sold at Cortoline?

A. 42%
B. 43%
C. 44%
D. 46%
E. 47%


Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let x = the percentage of gas sold at Cortoline
This means that 100-x = the percentage of gas sold at Petrocort

As far as PROPORTIONS go, x/100 is the proportion of gas sold at Cortoline
And (100-x)/100 is the proportion of gas sold at Petrocort

Now plug the values into the weighted averages formula.
We get: 2.99 = (x/100)(3.28) + [(100-x)/100][2.78]
Eliminate the fractions by multiplying both sides by 100 to get: 299 = (x)(3.28) + (100-x)[2.78]
Expand to get: 299 = 3.28x + 278 - 2.78x
Simplify: 299 = 0.5x + 278
Subtract 278 from both sides: 21 = 0.5x
Solve: x = 42

Answer: A

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Re: The city of Cortisville has two gas stations, Petrocort and Cortoline.  [#permalink]

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New post 22 Feb 2017, 11:53
P(2.78)----------C(3.28) is 0.5$ apart.

Weighted average is 2.99 which is 0.29$ away from Cortisville and 0.21$ away from Petrocort. So the weightage should be inversely proportional to this. Cortisville sold 0.21/0.50 = 42 % gasoline.

Answer is A
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Re: The city of Cortisville has two gas stations, Petrocort and Cortoline.  [#permalink]

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New post 06 Dec 2019, 17:51
How far is the average from either values ?
so, that is
2.99 - 2.78 = 0.21
2.99 - 3.28 = -0.29

So, for this we can try
x/100 ( 0.21) - y/100 ( 0.29) = 0
now, you can try plugging in values,

here A makes this 0
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Re: The city of Cortisville has two gas stations, Petrocort and Cortoline.   [#permalink] 06 Dec 2019, 17:51
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