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# After 4,000 gallons of water were added to a large water tan

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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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We can set up the following equation for the info in the question:

3/4 of x+4000=4/5 of x; where x is the capacity of the water tank.

x=80,000

We can alternatively work this out using proportion: we know that the additional 4000 gallons account for 4/5-3/4=1/20 of the tank. So if 4000 gallons account for 1/20 of the full tank, then 20/20 of the tank is 80,000.

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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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1/20x=4000..x=80000..
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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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x=tank capacity

4000/x = (4/5-3/4)/1
4000 = 1/20(x)
x=80000

Please vote for the best solutions by pressing Kudos button;
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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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Kudos
Let us assume the total capacity of tank to be x.

Since the tank was already filled to 3/4th(or 75%) of its capacity and 4,000 gallons of water were added to bring it to 4/5 th(or 80%) of its capacity, we can make the following inference:
5% of capacity(80%-75%) = 4000;
(5/100) * x = 4,000
x = 80,000;

Ans is (E).
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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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SOLUTION

After 4,000 gallons of water were added to a large water tank that was already filled to 3/4 of its capacity, the tank was then at 4/5 of its capacity. How many gallons of water does the tank hold when filled to capacity?

(A) 5,000
(B) 6,200
(C) 20,000
(D) 40,000
(E) 80,000

4,000 gallons of water comprise 4/5 - 3/4 = 1/20, which makes the capacity of the tank equal to 4,000*20 = 80,000 gallons.

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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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After 4,000 gallons of water were added to a large water tank that was already filled to 3/4 of its capacity, the tank was then at 4/5 of its capacity. How many gallons of water does the tank hold when filled to capacity?

(A) 5,000
(B) 6,200
(C) 20,000
(D) 40,000
(E) 80,000

$$\frac{3}{4}$$ of Tank = 75% of Tank

$$\frac{4}{5}$$ of Tank = 80% of Tank

Given that, difference between 80% and 75% of Tank is 4000 gallons
Or, 5% of Tank = 4000 gallons

Or, Full capacity of Tank $$= 20 * 4000 = 80000$$ gallons of water

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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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Kudos
Let full capacity of tank = x

3/4th of full capacity $$= \frac{3x}{4}$$

Addition of 4000 gallons $$= \frac{3x}{4} + 4000$$

Given that addition of water takes the level to 4/5th

$$\frac{3x}{4} + 4000 = \frac{4x}{5}$$

x = 4000 * 20

= 80000
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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
Let x be the capacity of tank

(4/5 - 3/4) x = 4000
(0.8-0.75)x = 4000
0.05 x = 4000
x = 4000 * 20 = 80,000
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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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Kudos
Nice Question
Here making an algebraic equation => [3/4] X +4000 = [4/5]X => X=80000
Smash E
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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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Kudos
3/4*x+4000=4/5*x
Solving for x, and getting x = 80K
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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
Let the currently existing water be x
Total capacity be y

$$\frac{x}{y} = \frac{3}{4}$$

$$\frac{x+4000}{y} = \frac{4}{5}$$

$$\frac{x}{y} + \frac{4000}{y} = \frac{4}{5}$$

$$\frac{3}{4} + \frac{4000}{y} = \frac{4}{5}$$

$$\frac{4000}{y} = \frac{1}{20}$$

y = 80,000

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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
Tank is filled to 3/4 capacity, so 1/4 is empty.
After adding 4000, Tank is filled to 4/5 capacity.
So T/4 > 4000 (Tank is still not filled to full capacity even after adding 4000)
T>16,000
we can reject atleast A, B using this logic
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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
$$\frac{3}{4}$$ $$x$$ + 4000 = $$\frac{4}{5}$$ $$x$$

$$\frac{4}{5}$$ $$x$$ - $$\frac{3}{4}$$ $$x$$ = 4000

$$\frac{1}{ 20}$$ * $$x$$ = 4000

$$x$$ = $$4000 * 20$$ = $$80,000$$
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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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Re: After 4,000 gallons of water were added to a large water tan [#permalink]
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