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

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Math Expert
Joined: 02 Sep 2009
Posts: 49275
If the current price per gallon of gas were to be decreased by approxi  [#permalink]

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21 Jan 2018, 03:43
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Difficulty:

35% (medium)

Question Stats:

74% (01:29) correct 26% (02:09) wrong based on 38 sessions

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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

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

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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) _________________ You've got what it takes, but it will take everything you've got Director Joined: 09 Mar 2016 Posts: 870 If the current price per gallon of gas were to be decreased by approxi [#permalink] ### Show Tags 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

$$\frac{66}{30} = 2,2$$

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

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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 &nbs [#permalink] 21 Jan 2018, 09:56
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