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A container is full. After 4/5 liters of its contents
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03 Apr 2017, 03:29
03 Apr 2017, 03:29
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83% (01:22) correct
16% (01:36) wrong based on 56 sessions
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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
Question: 12
Page: 320
Show: :: OA
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Re: A container is full. After 4/5 liters of its contents
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04 Apr 2017, 10:20
04 Apr 2017, 10:20
2
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:
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15 liters
Cheers,
Brent
Re: A container is full. After 4/5 liters of its contents
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09 Mar 2022, 15:50
09 Mar 2022, 15:50
1
Get common denominators for 4/5 and 3/4.
You end up with 16/20 and 15/20 so there was an overall change of 1/20.
Since 3 liters were taken out you know that 3 liters equals 1/20 of the total container.
3 liters multiplied times 20 equals a total capacity of 60 liters.
Multiply 4/5 by 60 and you get 48 initial liters in the container.
Subtract the 3 liters from the 48 and you get 45 so you need to add 15 liters to the container to refill it entirely.
You end up with 16/20 and 15/20 so there was an overall change of 1/20.
Since 3 liters were taken out you know that 3 liters equals 1/20 of the total container.
3 liters multiplied times 20 equals a total capacity of 60 liters.
Multiply 4/5 by 60 and you get 48 initial liters in the container.
Subtract the 3 liters from the 48 and you get 45 so you need to add 15 liters to the container to refill it entirely.
