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The concentration of a certain chemical in a full water tank

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joemama142000
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The concentration of a certain chemical in a full water tank [#permalink] New post   Updated on: 02 Mar 2014, 04:36
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The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is \(3 + \frac{4}{\sqrt{5-x}}\) parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft
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E

Originally posted by joemama142000 on 16 Nov 2005, 18:58.
Last edited by Bunuel on 02 Mar 2014, 04:36, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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The concentration of a certain chemical in a full water tank [#permalink] New post   10 Feb 2018, 20:37
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joemama142000 wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is \(3 + \frac{4}{\sqrt{5-x}}\) parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

OCDianaOC wrote:
Can you show me step-by-step how to solve this one? I'm missing something...

OCDianaOC - This question's wording is not easy. I rephrased it.

Given: a chemical concentration of 6
Given: a formula that will tell how deep the water is at a particular concentration, IF we have the concentration (we do)
Formula: \(3 + \frac{4}{\sqrt{5-x}}\)

Set the formula equal to concentration. The concentration of 6, in tandem with the formula, will yield depth.

\(3 + \frac{4}{\sqrt{5-x}} =\\
6\)
Subtract 3 from both sides:

\(\frac{4}{\sqrt{5-x}} = 3\)
Square both sides:

\((\frac{4^2}{(\sqrt{5-x})^2}) = 3^2\)

\((\frac{16}{(5-x)}) = 9\)
Multiply both sides by denominator and solve:

\(16 = 9(5 - x)\)
\(16 = 45 - 9x\)
\(9x = 29\)

\(x = \frac{29}{9} = 3.2\) feet

Answer E

Hope that helps. :-)

**The language "where 0 < x < 4," is mostly irrelevant. It's to keep the denominator in the formula positive. (Can't divide by zero, can't take the square root of a negative number.)
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Re: The concentration of a certain chemical in a full water tank [#permalink] New post   02 Mar 2014, 04:40
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PeterHAllen wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is \(3 + \frac{4}{\sqrt{5-x}}\) parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

My brain is cloudy, going to gym to clear it up....but how did you guys know to set the equation equal to 6? Once we get to the equation the math is easy but I did not know where to begin. Can someone explain?


Given: at a depth that is x feet below the top of the tank, the concentration is \(3 + \frac{4}{\sqrt{5-x}}\) parts per million.

Question: at what depth, for which x, is the concentration equal to 6 parts per million? So, for which x, is \(3 + \frac{4}{\sqrt{5-x}}\) equal to 6?

\(3 + \frac{4}{\sqrt{5-x}}=6\) --> \(x\approx{3.2}\).

Answer: E.

Hope it's clear.
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[#permalink] New post   16 Nov 2005, 19:39
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3 + 4/sqrt(5-x) = 6

4/sqrt(5-x) = 3

16/(5-x) = 9

9x = 29 -> x = 3.2
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[#permalink] New post   16 Nov 2005, 19:48
I was going to go with 3.0...but then the question says witin 0.1 feet...and with 3.0..we get within 0.2 feet...so I would have just picked 3.2 at that point....

anyway

4/sqrt(5-x)=3

16/(5-x)=9

16=45-9x

solve for X...
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Re: Problem Solving Proportion [#permalink] New post   16 Nov 2005, 19:49
joemama142000 wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is 3 + 4/sqrt(5-x) parts per million, where 0< x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

A) 2.4 ft
B) 2.5 ft
C) 2.8 ft
D) 3.0 ft
E) 3.2 ft


3 + 4/sqrt(5-x) = 6

solve for x, x = 29/9 = 3.2 ft

E
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[#permalink] New post   16 Nov 2005, 19:49
fresinha12 wrote:
I was going to go with 3.0...but then the question says witin 0.1 feet...and with 3.0..we get within 0.2 feet...so I would have just picked 3.2 at that point....
anyway
4/sqrt(5-x)=3
16/(5-x)=9
16=45-9x
solve for X...


You are tired. Go to bed :sleeping:
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[#permalink] New post   16 Nov 2005, 19:51
not yet...its raining here...and I want to go to the gym

to go or not to go to gym is the question...what would GSR do?hmm

gsr wrote:
fresinha12 wrote:
I was going to go with 3.0...but then the question says witin 0.1 feet...and with 3.0..we get within 0.2 feet...so I would have just picked 3.2 at that point....
anyway
4/sqrt(5-x)=3
16/(5-x)=9
16=45-9x
solve for X...


You are tired. Go to bed :sleeping:
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[#permalink] New post   16 Nov 2005, 19:57
Thumbs up! for a 'go' to gym!
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[#permalink] New post   16 Nov 2005, 20:00
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gym it is...see you in an hr...

gsr wrote:
Thumbs up! for a 'go' to gym!
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Re: The concentration of a certain chemical in a full water tank [#permalink] New post   01 Mar 2014, 13:11
My brain is cloudy, going to gym to clear it up....but how did you guys know to set the equation equal to 6? Once we get to the equation the math is easy but I did not know where to begin. Can someone explain?
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Re: The concentration of a certain chemical in a full water tank [#permalink] New post   29 Sep 2015, 03:32
I've been trying to wrap my head around how to set up that equation, but am not able to. Could someone please help me out with why I should be equating 6ppm with the concentration at x feet? :(
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Re: The concentration of a certain chemical in a full water tank [#permalink] New post   10 Feb 2018, 15:46
Can you show me step-by-step how to solve this one? I'm missing something...
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Re: The concentration of a certain chemical in a full water tank [#permalink] New post   10 Feb 2018, 20:49
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generis wrote:
joemama142000 wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is \(3 + \frac{4}{\sqrt{5-x}}\) parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft

OCDianaOC wrote:
Can you show me step-by-step how to solve this one? I'm missing something...

OCDianaOC - This question's wording is not easy. I rephrased it.

Given: a chemical concentration of 6
Given: a formula that will tell how deep the water is at a particular concentration, IF we have the concentration (we do)
Formula: \(3 + \frac{4}{\sqrt{5-x}}\)

Set the formula equal to concentration. The concentration of 6, in tandem with the formula, will yield depth.

\(3 + \frac{4}{\sqrt{5-x}} =\\
6\)
Subtract 3 from both sides:

\(\frac{4}{\sqrt{5-x}} = 3\)
Square both sides:

\((\frac{4^2}{(\sqrt{5-x})^2}) = 3^2\)

\((\frac{16}{(5-x)}) = 9\)
Multiply both sides by denominator and solve:

\(16 = 9(5 - x)\)
\(16 = 45 - 9x\)
\(9x = 29\)

\(x = \frac{29}{9} = 3.2\) feet

Answer E

Hope that helps. :-)

**The language "where 0 < x < 4," is mostly irrelevant. It's to keep the denominator in the formula positive. (Can't divide by zero, can't take the square root of a negative number.)


YAAAAY! Your explanation is perfect. I finally understand how to solve this now! :-)

Thank you!
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Re: The concentration of a certain chemical in a full water tank [#permalink] New post   21 Aug 2019, 05:07
joemama142000 wrote:
The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is \(3 + \frac{4}{\sqrt{5-x}}\) parts per million, where 0 < x < 4. To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

(A) 2.4 ft
(B) 2.5 ft
(C) 2.8 ft
(D) 3.0 ft
(E) 3.2 ft


Given: The concentration of a certain chemical in a full water tank depends on the depth of the water. At a depth that is x feet below the top of the tank, the concentration is \(3 + \frac{4}{\sqrt{5-x}}\) parts per million, where 0 < x < 4.

Asked: To the nearest 0.1 foot, at what depth is the concentration equal to 6 parts per million?

6 = \(3 + \frac{4}{\sqrt{5-x}}\)
\(\sqrt{4}{\sqrt{5-x}} = 3\)
5-x = 16/9 = 1.8 to the nearest .1 foot
x = 5 -1.8 = 3.2 to the nearest .1 foot

IMO E
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Re: The concentration of a certain chemical in a full water tank [#permalink] New post   14 Jun 2023, 13:14
Shouldn't the answer be total -x = depth of water.
The water depth is given as x feet below the top of the tank.

When we equate the equation with 6 and derive at an answer, then the value gives the depth from the top of the tank. inorder to dervice at water depth, we will have to do total depth - top of the depth

Please correct my understanding.
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Re: The concentration of a certain chemical in a full water tank [#permalink] New post   15 Jun 2023, 00:55
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nikitathegreat wrote:
Shouldn't the answer be total -x = depth of water.
The water depth is given as x feet below the top of the tank.

When we equate the equation with 6 and derive at an answer, then the value gives the depth from the top of the tank. inorder to dervice at water depth, we will have to do total depth - top of the depth

Please correct my understanding.


The depth of the water is measured from the top of the tank to the bottom. Hence, those are the same.
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Re: The concentration of a certain chemical in a full water tank [#permalink]
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