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A tank holds x gallons of a saltwater solution that is 20% [#permalink]

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22 Feb 2008, 16:33

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A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 10 Gallons of water and 20 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?

A. 37.5 B. 75 C. 100 D. 150 E. 175

Can you show me how to solve this without backsolving, ie the real algabraic way?

Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.

Original mixture has 20% salt and 80% water. Total = x Out of which Salt = 0.2x and water = 0.8x Now, 1/4 water evaporates and all salt remains. So what remains is 0.2x salt and 0.6x water. Now 20 gallons salt is added and 10 gallons of water is added. So salt now becomes -> (0.2x + 20) and water --> (0.6x+10) Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water. So (0.2x+20) = (0.6x+10)/2, Solving, x = 150.

Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.

Original mixture has 20% salt and 80% water. Total = x Out of which Salt = 0.2x and water = 0.8x Now, 1/4 water evaporates and all salt remains. So what remains is 0.2x salt and 0.6x water. Now 20 gallons salt is added and 10 gallons of water is added. So salt now becomes -> (0.2x + 20) and water --> (0.6x+10) Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water. So (0.2x+20) = (0.6x+10)/2, Solving, x = 150.

Outstanding response. thank you. Can you describe how you started unpeeling this? I found the question wording really confusing.

Also, what level difficulty would you say this is?

Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.

Original mixture has 20% salt and 80% water. Total = x Out of which Salt = 0.2x and water = 0.8x Now, 1/4 water evaporates and all salt remains. So what remains is 0.2x salt and 0.6x water. Now 20 gallons salt is added and 10 gallons of water is added. So salt now becomes -> (0.2x + 20) and water --> (0.6x+10) Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water. So (0.2x+20) = (0.6x+10)/2, Solving, x = 150.

Quote:

Outstanding response. thank you. Can you describe how you started unpeeling this? I found the question wording really confusing.

Also, what level difficulty would you say this is?

Thanks. Actually , I did not solve it backwards. I solved it as per the flow given in the problem question. Honestly, I dont think this was more than a 650 level question.

Re: A tank holds x gallons of a saltwater solution that is 20% [#permalink]

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15 Feb 2014, 17:40

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Re: A tank holds x gallons of a saltwater solution that is 20% [#permalink]

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18 Apr 2014, 14:01

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Understand the logic of the flow of question.

Consider X initial solution.

0.2X = Salt 0.8X = Water

1/4(0.8X)= Evaporated Leaving 0.6X=water

0.6X+10=Water 0.2X+20=Salt

Salt concentration now becomes= 1/3 of the Solution

(0.2X+20)/(0.8X+30) = 1/3

X=150
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A tank holds x gallons of a saltwater solution that is 20% [#permalink]

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07 Nov 2015, 09:57

A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 10 Gallons of water and 20 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?

A. 37.5 B. 75 C. 100 D. 150 E. 175

after evaporation, x-(.25)(.8)x=.8x gallons salt now=25% of .8x gallons water now=75% of .8x gallons (.25)(.8x)+20=(.8x+30)/3 x=150 gallons D

Last edited by gracie on 23 Sep 2017, 20:25, edited 1 time in total.

Re: A tank holds x gallons of a saltwater solution that is 20% [#permalink]

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27 Jun 2016, 07:12

Manbehindthecurtain wrote:

A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 10 Gallons of water and 20 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?

A. 37.5 B. 75 C. 100 D. 150 E. 175

Can you show me how to solve this without backsolving, ie the real algabraic way?

Got the right answer but the wording is super bad! _________________

Re: A tank holds x gallons of a saltwater solution that is 20% [#permalink]

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06 Sep 2017, 01:15

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x gallon was solution = 0.2x salt and 0.8x water, 0.25% evaporated = 0.6x water remains new solution is 0.2x salt and 0.6x water 20 gallon salt is added, new salt = 20+0.2x 10 gallon water added , new water = 10+0.6x total solution = 30+0.8x

Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

Re: A tank holds x gallons of a saltwater solution that is 20% [#permalink]

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06 Sep 2017, 02:46

Manbehindthecurtain wrote:

A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 10 Gallons of water and 20 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?

A. 37.5 B. 75 C. 100 D. 150 E. 175

Can you show me how to solve this without backsolving, ie the real algabraic way?

It can be easily solved by front solving.

Salt Water Total 0.2x 0.8x x After Evaporation 0.2x 0.6x 0.8x After adding 10 gallons of water and 20 gallons of salt 20+0.2x 10+0.6x 30+0.8x

20+0.2x )/ (30+0.8x = 1/3 x = 150

Very Simple . Will take around 1 minute 40 seconds
_________________

A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 10 Gallons of water and 20 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?

A. 37.5 B. 75 C. 100 D. 150 E. 175

We are given that a tank holds x gallons of a saltwater solution that is 20% salt by volume. Thus, the solution contains 0.2x salt and 0.8x water. After 1/4 of the water is evaporated, there is 0.6x water left.

We are also given that when 10 gallons of water and 20 gallons of salt are added, the resulting mixture is 33 1/3% (or 1/3) salt by volume. Thus:

(0.2x + 20)/(0.2x + 0.6x + 10 + 20) = 1/3

(0.2x + 20)/(0.8x + 30) = 1/3

Multiplying 10/10 on the left side of the equation, we have:

(2x + 200)/(8x + 300) = 1/3

8x + 300 = 6x + 600

2x = 300

x = 150

Answer: D
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Re: A tank holds x gallons of a saltwater solution that is 20% [#permalink]

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17 Sep 2017, 06:32

A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 10 Gallons of water and 20 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?

Initially the solution contains 0.8x of water and 0.2x of salt. 1/4th of the water is evaporated which is (1/4*0.8x) = x/5. Hence, 1-x/5= 4x/5 is the remaining content of solution. 20 gallons of salt is added , hence, new salt content in solution= 0.2x+20 Total content = 4x/5+30

0.2x+20/4x/5+30 = 1/3 Solving for x, we get x=150. (option D)