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The Crandall’s hot tub has a capacity of x liters and is half full. Th 13 Mar 2020, 04:51
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C
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69% (02:08) correct 31% (02:06) wrong based on 524 sessions

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The Crandall’s hot tub has a capacity of x liters and is half full. Their swimming pool, which has a capacity of y liters, is filled to four-fifths of its capacity. If enough water is drained from the swimming pool to fill the hot tub to capacity, the pool is now how many liters short of full capacity, in terms of x and y ?

(A) 0.8y − 0.5x
(B) 0.8y + 0.5x
(C) 0.2y + 0.5x
(D) 0.3(y − x)
(E) 0.3(y + x)
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C
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The Crandall’s hot tub has a capacity of x liters and is half full. Th 13 Mar 2020, 06:41
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Bunuel
The Crandall’s hot tub has a capacity of x liters and is half full. Their swimming pool, which has a capacity of y liters, is filled to four-fifths of its capacity. If enough water is drained from the swimming pool to fill the hot tub to capacity, the pool is now how many liters short of full capacity, in terms of x and y ?

(A) 0.8y − 0.5x
(B) 0.8y + 0.5x
(C) 0.2y + 0.5x
(D) 0.3(y − x)
(E) 0.3(y + x)
Show more


    • Total capacity of hot tub = x liters
      o Tub currently filled = 0.5* x
         Amount of water needed to fill it to full capacity = x – 0.5x = 0.5x
    • Capacity of pool = y liters
      o Pool currently filled = 4/5 * y = 0.8y liters
    • The tub is completely filled using the pool water, so amount of water used from the pool = 0.5x
      o Thus, amount of water left in the pool = 0.8y – 0.5x.

To fill the pool to full capacity we would need
    = Total capacity of pool – Current water in the pool
    = y – (0.8y – 0.5x)
    = 0.2y + 0.5x
Thus, the correct answer is Option C.
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The Crandall’s hot tub has a capacity of x liters and is half full. Th 13 Jun 2021, 23:01
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IMO C
simple method

the pool is now 4y/5 full means 1y/5 empty

we need to take x/2 water more to fill the tub .that will be emptied from pool

implies

total empty =1y/5 + x/2=.2y+.5x
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The Crandall’s hot tub has a capacity of x liters and is half full. Th 12 Jun 2022, 19:50
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Bunuel
The Crandall’s hot tub has a capacity of x liters and is half full. Their swimming pool, which has a capacity of y liters, is filled to four-fifths of its capacity. If enough water is drained from the swimming pool to fill the hot tub to capacity, the pool is now how many liters short of full capacity, in terms of x and y ?

(A) 0.8y − 0.5x
(B) 0.8y + 0.5x
(C) 0.2y + 0.5x
(D) 0.3(y − x)
(E) 0.3(y + x)
Show more

I think simplest method would be to use smart numbers to plug into x and y. Since we are dealing with fractions half (1/2) and 4/5, so a good smart number to choose for both x and y is 10
So, hot tub is 10L and currently 5L full. Pool is 10L but currently 8L full. Water drained from pool to fill hot tub fully. Hot tub needs 5L more
so Pool now has 8-5 = 3L, which means it is 7L short of full capacity
Plug x and y as 10 in answer choices, we get C = 0.2y + 0.5x = 2+5 = 7 hence C
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The Crandall’s hot tub has a capacity of x liters and is half full. Th 03 Jun 2025, 15:55
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