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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

Respuesta :

Answer:  The correct option is

(E) 80,000.

Step-by-step explanation:  Given that after adding 4,000 gallons of water to a large tank that was already filled to [tex]\dfrac{3}{4}[/tex] of its capacity, the tank was then at [tex]\drac{4}{5}[/tex] of its capacity.

We are to find the number of gallons of water that the tank hold when filled to capacity.

Let the tank can hold x gallons of water when filled to capacity.

Then, according to the given information, we have

[tex]\dfrac{3}{4}x+4000=\dfrac{4}{5}x\\\\\\\Rightarrow \dfrac{4}{5}x-\dfrac{3}{4}x=4000\\\\\\\Rightarrow \dfrac{16-15}{20}x=4000\\\\\Rightarrow x=4000\times20\\\\\Rightarrow x=80000.[/tex]

Thus, the required capacity of the tank is 80,000 gallons of water.

Option (E) is CORRECT.

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