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A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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23 May 2016, 21:56

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C

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A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?

Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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24 May 2016, 05:20

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nalinnair wrote:

A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container? A. 4\(\frac{1}{2}\) B. 4 C. 3\(\frac{3}{4}\) D. 3 E. 1\(\frac{1}{4}\)

Let x be the amount of solution in 6lit container and (5-x) is the amount in 2 lit solution.

The question stem says that both containers are filled to equal % of their capacity

x is what % of 6= 100x/6 5-x is what % of 2= 100 (5-x)/2

100x/6= 100(5-x)/2 x= 15/4= 3\(\frac{3}{4}\)

C is the answer
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A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container? A. 4\(\frac{1}{2}\) B. 4 C. 3\(\frac{3}{4}\) D. 3 E. 1\(\frac{1}{4}\)

Hi,

Another way-

since the different capacity containers contain same proportion, it will be the SAME as proportion in SUM of these quantities.. so Proportion is 5 liters in (2+6) or 8 ltr container......so \(Proportion = \frac{5}{8}\)... with this proportion quantity in 6 ltr container = \(6*\frac{5}{8}= \frac{15}{4} = 3 \frac{3}{4}\) C
_________________

A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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24 May 2016, 13:52

A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?

A. 41212

B. 4

C. 33434

D. 3

E. 114

let x=% of capacity 5=2x+6x=8x x=5/8 5/8*6=3 3/4 liters C

Last edited by gracie on 09 Oct 2017, 10:08, edited 1 time in total.

Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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19 Feb 2017, 20:34

Another way to do this problem is to WORK BACKWARDS. Start with the two easy numbers 4 and 3. Now if u pick 4, that means 4 liters go into the 6 liter container and 1 liter goes into the 2 liter container. So that is 2/3 of capacity in 6l container and 1/2 capacity in 2l container. Now work with 3. 3 in 6l and 2 in 2l. That is, 1/2 of capacity in 6l and full capacity in 2l. Now for 4, 6l went greater than 2l in % capacity and when we used 3, 2l container went in greater % of capacity. Hence the only option that would satisfy this is 3 3/4 which lies in the middle of these capacities!

Re: A total of 5 liters of gasoline is to be poured into two empty contain [#permalink]

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20 Feb 2017, 04:34

chetan2u wrote:

nalinnair wrote:

A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container? A. 4\(\frac{1}{2}\) B. 4 C. 3\(\frac{3}{4}\) D. 3 E. 1\(\frac{1}{4}\)

Hi,

Another way-

since the different capacity containers contain same proportion, it will be the SAME as proportion in SUM of these quantities.. so Proportion is 5 liters in (2+6) or 8 ltr container......so \(Proportion = \frac{5}{8}\)... with this proportion quantity in 6 ltr container = \(6*\frac{5}{8}= \frac{15}{4} = 3 \frac{3}{4}\) C

Hi chetan your explanation is easy can you please tell if it will be for smaller container will the logic be 2*5/8 mean 5/4 or 1*1/4 ??
_________________

A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?

A. 4\(\frac{1}{2}\)

B. 4

C. 3\(\frac{3}{4}\)

D. 3

E. 1\(\frac{1}{4}\)

Solution:

Since the 6-liter container is 3 times the capacity of the 2-liter container, we want to pour 3 times as much gasoline into the 6-liter container as into the 2-liter container. We can let x = the amount of gasoline poured into the 2-liter container; thus, 3x = the amount of gasoline poured into the 6-liter container. We can solve for x using the following equation:

x + 3x = 5

4x = 5

x = 5/4

Thus, the amount of gasoline that should be poured into the 6-liter container is 3 x 5/4 = 15/4 = 3 ¾ liters.

Alternate Solution:

Let x denote the amount of gasoline poured into the 6-liter container. Since the percentages of gasoline in each container must be the same, we must have:

x/6 = (5-x)/2

2x = 30 - 6x

8x = 30

x = 30/8 = 3 ¾

Answer: C
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