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If the current price per gallon of gas were to be decreased by approxi

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If the current price per gallon of gas were to be decreased by approxi  [#permalink]

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New post 21 Jan 2018, 03:43
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

72% (02:18) correct 28% (02:44) wrong based on 43 sessions

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If the current price per gallon of gas were to be decreased by approxi  [#permalink]

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New post 21 Jan 2018, 07:06
Bunuel wrote:
If the current price per gallon of gas were to be decreased by approximately 25 percent, 10 more gallons could be bought for $66. What is the current price per gallon of gas?

A. $1.45
B. $1.65
C. $1.80
D. $2.20
E. $2.40


Since the price of the gas will be reduced by 25%, if the initial price was 4x,
the price of gas will become 3x(75% of the old price) and at this price, 10
extra gallons could be bought for the same price.

We can construct the following equations

(1) \(4x*y = 66 => y = \frac{66}{4x}\)
(2) \(3x*(y+10) = 66 -> 3xy + 30x = 66\)

Substituting the value of y from (1) in equation (2), we get

\(\frac{3x*66}{4x} + 30x = 66\) -> \(30x = 66 - \frac{3*66}{4} = \frac{66}{4}\) -> \(x = \frac{66}{30*4} = \frac{11}{20}\)

Therefore, the initial cost of a gallon of gas is \(4x = 4*\frac{11}{20}\) = 2.2$(Option D)


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If the current price per gallon of gas were to be decreased by approxi  [#permalink]

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New post 21 Jan 2018, 09:31
Bunuel wrote:
If the current price per gallon of gas were to be decreased by approximately 25 percent, 10 more gallons could be bought for $66. What is the current price per gallon of gas?

A. $1.45
B. $1.65
C. $1.80
D. $2.20
E. $2.40



Hi everyone :) here is my solution:) finally solved somthing myself lol

Let price per gallon be \(X\)

Let total number of gallons \(Y\)

Total cost \(x*y = $66\) ---> price per gallon \(x= \frac{66}{y}\) <---- equation #1

If we reduce the price X by 25%, we can purchase +10 ballons for the same budget

hence: \((X - 0,25X) *(y+10) = 66\) < --- now put equation #1 into this one.

\(\frac{66}{y}\)- \(\frac{66*0.25}{y}\)*\((y+10)\) = \(66\)

\(\frac{49,5}{y}\) * \((y+10) = 66\)

\(\frac{49,5 (y+10)}{y}\) = \(66\) (cross multiply)

\(49,5y+495 = 66y\)

\(495 = 16,5y\)

\(y = 30\)

So total quantity of gallons is 30

\(\frac{66}{30} = 2,2\)

Answer: D :)
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Re: If the current price per gallon of gas were to be decreased by approxi  [#permalink]

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New post 21 Jan 2018, 09:56
Answer is D. Solution is 66 for 10 gallons. Price per gallon 6.6. this is 75 pc of the price. So original price is 6.6/75*100 i.e 8.8. so the increase in price is 8.8-6.6 that is 2.2

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Re: If the current price per gallon of gas were to be decreased by approxi   [#permalink] 21 Jan 2018, 09:56
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