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If 75 gallons of water were added to a pool that is half full, the poo

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Bunuel
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If 75 gallons of water were added to a pool that is half full, the poo [#permalink] New post   23 Oct 2019, 01:22
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If 75 gallons of water were added to a pool that is half full, the pool would then be 2/3 full. How many gallons of water does the pool hold when it is full?

A. 300
B. 360
C. 420
D. 450
E. 525
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D
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Re: If 75 gallons of water were added to a pool that is half full, the poo [#permalink] New post   23 Oct 2019, 02:08
Bunuel wrote:
If 75 gallons of water were added to a pool that is half full, the pool would then be 2/3 full. How many gallons of water does the pool hold when it is full?

A. 300
B. 360
C. 420
D. 450
E. 525


Asked: If 75 gallons of water were added to a pool that is half full, the pool would then be 2/3 full. How many gallons of water does the pool hold when it is full?

2/3 - 1/2 = 1/6

Let the capacity of the pool be x
x/6 = 75
x = 450

IMO D
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Re: If 75 gallons of water were added to a pool that is half full, the poo [#permalink] New post   23 Oct 2019, 02:17
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Bunuel wrote:
If 75 gallons of water were added to a pool that is half full, the pool would then be 2/3 full. How many gallons of water does the pool hold when it is full?

A. 300
B. 360
C. 420
D. 450
E. 525


from given info
75+x/2=2x/3
solve for x= 450
IMO D
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EgmatQuantExpert
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If 75 gallons of water were added to a pool that is half full, the poo [#permalink] New post   23 Oct 2019, 05:20
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Solution


Given:
    • 75 gallons of water were added to a pool that is half full
      o The pool would then be \(\frac{2}{3}\) full

To find:
    • How many gallons of water does the pool hold when it is full?

Approach and Working Out:
    • 75 gallons of water fills \(\frac{2}{3} – \frac{1}{2} = \frac{1}{6}^{th}\) of the tank

Therefore, a full tank holds 6 * 75 gallons of water = 450 gallons

Hence, the correct answer is Option D.

Answer: D
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Re: If 75 gallons of water were added to a pool that is half full, the poo [#permalink] New post   23 Oct 2019, 08:20
Bunuel wrote:
If 75 gallons of water were added to a pool that is half full, the pool would then be 2/3 full. How many gallons of water does the pool hold when it is full?

A. 300
B. 360
C. 420
D. 450
E. 525


Let the total capacity of the pool be 6x

Now, \(3x + 75 = 4x\)

Or, \(x = 75\)

So, The total capacity of the pool is \(75*6 = 450\) , Answer must be (D)
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Re: If 75 gallons of water were added to a pool that is half full, the poo [#permalink] New post   27 Oct 2019, 19:52
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Bunuel wrote:
If 75 gallons of water were added to a pool that is half full, the pool would then be 2/3 full. How many gallons of water does the pool hold when it is full?

A. 300
B. 360
C. 420
D. 450
E. 525


We can let n = the full capacity of the pool, in gallons, and create the equation:

75 + n/2 = 2n/3

Multiplying by 6, we have:

450 + 3n = 4n

450 = n

Alternate Solution:

When we add the 75 gallons, the pool’s capacity has increased from ½ to ⅔. Thus, 75 gallons is (⅔ - ½) = 4/6 - 3/6 = 1/6 of the entire capacity of the pool. Thus, the total capacity of the pool is 75 x 6 = 450 gallons.

Answer: D
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Re: If 75 gallons of water were added to a pool that is half full, the poo [#permalink] New post   28 Jun 2021, 07:58
Bunuel wrote:
If 75 gallons of water were added to a pool that is half full, the pool would then be 2/3 full. How many gallons of water does the pool hold when it is full?

A. 300
B. 360
C. 420
D. 450
E. 525

\(\frac{x}{2} + 75 = \frac{2x}{3}\)

Or, \(75 = \frac{2x}{3} - \frac{x}{2}\)

Or, \(75 = \frac{4x -3x}{6}\)

Or, \(x = 450\), Answer must be (D)
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Re: If 75 gallons of water were added to a pool that is half full, the poo [#permalink] New post   03 Jul 2021, 13:58
EgmatQuantExpert why has this been subtracted 2/3 - 1/2?
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Re: If 75 gallons of water were added to a pool that is half full, the poo [#permalink]
03 Jul 2021, 13:58
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