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

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

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New post 08 Jan 2018, 23:54
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A
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C
D
E

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53% (05:13) correct 47% (03:31) wrong based on 15 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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Re: A gas station sells three grades of fuel High, Medium and Low. The sel [#permalink]

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

Let's start with finding the prices for each type of gallon:
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

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Re: A gas station sells three grades of fuel High, Medium and Low. The sel [#permalink]

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New post 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.

We'll start with the median answer - C.
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.
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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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