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A container is full. After 4/5 liters of its contents

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Joined: 07 Jun 2014
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A container is full. After 4/5 liters of its contents [#permalink] New post 03 Apr 2017, 03:29
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Question Stats:

66% (01:11) correct 33% (00:00) wrong based on 3 sessions
A container is \(\frac{4}{5}\) full. After 3 liters of its contents are poured out, the container is \(\frac{3}{4}\) full. How many liters would need to be poured back in to refill the container?

Drill 3
Question: 12
Page: 320


[Reveal] Spoiler: OA
15

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Re: A container is full. After 4/5 liters of its contents [#permalink] New post 04 Apr 2017, 10:20
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sandy wrote:
A container is \(\frac{4}{5}\) full. After 3 liters of its contents are poured out, the container is \(\frac{3}{4}\) full. How many liters would need to be poured back in to refill the container?


Let C = capacity of the container
We can write: (original volume of liquid) - 3 liters = (new volume of liquid)
Rewrite as: (4/5 of C) - 3 = (3/4 of C)
Or...: 4C/5 - 3 = 3C/4
Rearrange to get: 4C/5 - 3C/4 = 3
Rewrite with common denominators: 16C/20 - 15C/20 = 3
Simplify: C/20 = 3
Solve: C = 60

In other words, the container's capacity is 60 liters

If the container is 3/4 full, then the volume of liquid = 3/4 of 60 liters = 45 liters
So, we must add 15 more liters to fill the container.

Answer:
[Reveal] Spoiler:
15 liters


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Brent
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Re: A container is full. After 4/5 liters of its contents   [#permalink] 04 Apr 2017, 10:20
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