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# A gas station sells three grades of fuel High, Medium and Low. The sel

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
A gas station sells three grades of fuel High, Medium and Low. The sel  [#permalink]

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08 Jan 2018, 23:54
00:00

Difficulty:

45% (medium)

Question Stats:

60% (03:32) correct 40% (04:22) wrong based on 16 sessions

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A gas station sells three grades of fuel High, Medium and Low. The selling price of High grade is \$2.20 per gallon, which is 25 percent higher than that of Medium grade, while the price of Low grade is 75 percent of the selling price of Medium grade. If on a given day the station sells twice as much Low grade gas as Medium grade gas, and 4 times as much Medium grade gas as High grade gas, with total revenue of \$99, how many gallons of fuel did the station sell?

A. 130
B. 91
C. 78
D. 65
E. 39

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Intern
Joined: 28 Mar 2017
Posts: 4
Re: A gas station sells three grades of fuel High, Medium and Low. The sel  [#permalink]

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09 Jan 2018, 00:27
1
1
Hi everyone,

High - 2.2\$
Med - 2.2*4/5\$
Low - 2.2*4/5*3/4=2.2*3/5\$
Now, we will mark the quantity of High grade gallon as x and the other quantities according to this one.
High - x
Med - 4x
Low - 8x
Proceed with equation:
2.2x+2.2*4/5*4x+2.2*3/5*8x=99
9*2.2x=99
x=5
So, the total number of gallons is 5+20+40=65

ANS: D

examPAL Representative
Joined: 07 Dec 2017
Posts: 1153
Re: A gas station sells three grades of fuel High, Medium and Low. The sel  [#permalink]

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09 Jan 2018, 04:17
Bunuel wrote:
A gas station sells three grades of fuel High, Medium and Low. The selling price of High grade is \$2.20 per gallon, which is 25 percent higher than that of Medium grade, while the price of Low grade is 75 percent of the selling price of Medium grade. If on a given day the station sells twice as much Low grade gas as Medium grade gas, and 4 times as much Medium grade gas as High grade gas, with total revenue of \$99, how many gallons of fuel did the station sell?

A. 130
B. 91
C. 78
D. 65
E. 39

As word problems can be confusing, we'll use the answers!
This is an Alternative approach.

Since the ratio between gallons sold is 1:4:8 then each ratio unit is 78/13 = 6 gallons of gas.
Then the total revenue is
6*2.2 + 24*0.8*2.2 + 48*0.8*0.75*2.2 =
2.2*6(1+ 4*0.8 + 8*0.8*0.75) =
13.2(1+3.2+4.8) = 13.2*9 which is about 120.
Too much! (C) and the larger (B), (A) are eliminated.
Moreover, since (E) would mean decreasing the revenue by half, we know that it must be too small.
Then we can mark (D) and move on.

Just for practice, since 65/13 = 5, we can use our simplification from above to write:
2.2*5*9 = 11*9 = 99, as required.
_________________
Re: A gas station sells three grades of fuel High, Medium and Low. The sel   [#permalink] 09 Jan 2018, 04:17
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