How can i find the capacity of x? 2 containers, each 4/5 full of water...

[ashik110]

Two containers, x and y of the same capacity, are each 4/5 full of water. If 4 liters of water from container x is added to container y, the ratio of water in the two container becomes 2:3. What tis the capacity of container x?

Please help me to find out the capacity. How can i solve the question, please explain in detail.

 

[ksdhart2]

Well, when I'm faced with a difficult problem, I find it helpful to go back and carefully read every word of the problem text and parse out as much information as possible. Let's do that and see what we find.

Two containers, x and y of the same capacity

Alright. So now we know x = y.

are each 4/5 full of water.

If x and y represent the volumes of the full containers, then what expression represents "four-fifths full?"

If 4 liters of water from container x is added to container y

Four liters are taken from container x, so what expression represents its new volume? That four liters are added to container y, so what expression represents its new volume?

the ratio of water in the two container becomes 2:3

What equation can you create that represents that the ratio of the volume in container x to the volume in container y is 2:3?

Give it a try, and see how far you get. If you get stuck again, that's alright, but when you reply back please share with us any and all work you've done on this problem, even the parts you know for sure are wrong. Thank you.

 

[ashik110]

Well, when I'm faced with a difficult problem, I find it helpful to go back and carefully read every word of the problem text and parse out as much information as possible. Let's do that and see what we find.



Alright. So now we know x = y.



If x and y represent the volumes of the full containers, then what expression represents "four-fifths full?"



Four liters are taken from container x, so what expression represents its new volume? That four liters are added to container y, so what expression represents its new volume?



What equation can you create that represents that the ratio of the volume in container x to the volume in container y is 2:3?

Give it a try, and see how far you get. If you get stuck again, that's alright, but when you reply back please share with us any and all work you've done on this problem, even the parts you know for sure are wrong. Thank you.

i am figured out this equation 4x/5+4/ 4y/5-4=2/3. though x=y i can use 4x insted of 4y by solving i find x=16 and y=24 so the ratio is 2:3
so the capacity of x is 20?

 

[ksdhart2]

i am figured out this equation 4x/5+4/ 4y/5-4=2/3. though x=y i can use 4x insted of 4y by solving i find x=16 and y=24 so the ratio is 2:3
so the capacity of x is 20?

I'd note that you need to use grouping symbols, like so: (4x/5+4) / (4y/5-4)=2/3. Without those parentheses, what you wrote is:

\(\displaystyle \dfrac{4x}{5}+\dfrac{4}{4} \cdot \dfrac{y}{5}-4=\dfrac{2}{3}\)

Which I'm pretty sure isn't what you meant. That aside, your solution is almost correct. In the future, if you're ever unsure about an answer, you can always check it yourself by plugging it back into the original problem and seeing if it meets all of the criteria. Your proposed solution says that the capacity of each container is 20 liters. They start the problem 4/5 full, or with 20 * 4/5 = 16 liters in them. Four liters is then taken from container x and poured into container y. That means container x now has 16 - 4 = 12 liters in it. And container y has 16 + 4 = 20 liters in it. The ratio of 12 to 20 is 12/20 = 3/5. Whoops, that's not 2/3. So, that means your answer is correct. You're absolutely correct that the volumes of water after pouring should be 16 liters and 24 liters, respectively, though. So, can you see the one small error you made, and how to correct it?

 

[sean]

Two containers, x and y of the same capacity, are each 4/5 full of water. If 4 liters of water from container x is added to container y, the ratio of water in the two container becomes 2:3. What tis the capacity of container x?

So you know that the containers have the same amount of water at the start so the ratio is 1:1.

They pour 4 liters (for no particular reason) from container one into container 2 and now the ratio is 2:3. This actually means that if you added the water from the two containers together that it is 100%. container x is 2/5 of that water and container y is 3/5 of this water. You can kind of see this if you take the ratio as 2/5:3/5 (you add the 2 and 3 to get the denominator of the fraction). This is all well and good but what now?

Well we know that the difference between the two tanks is 8 liters. You take 4 from container x and add 4 to container y. We also know that that difference is 1/5 (difference between the water in x and y) of the over all water (both x and y together). So all the water amounts to 8 liters multiplied by 5 (8*5=40) so 40 liters.

We know they were equal at the start so each contained 20 liters. We also know that they were both 4/5 full so divide by 4 and multiply by 5 will give us 5/5 or the full capacity. Therefore the full capacity is 25 liters.

Hope this helps let me know if you've any questions.

 

[rony]

Kwick way (important on timed tests):

x = water in each at start

(x - 4) / (x + 4) = 2/3
Solve: x = 20
So container size = 5/4 * 20 = 25

Hi Denis, I want to know where you get 5/4?

 

[mmm4444bot]

Denis, I want to know where you get 5/4?

Denis changed the definition of symbol x.

Everyone else was using x to represent the requested volume.

Denis decided to go a different way:

x = 4/5*(requested volume)

Once he found his x, he solved the following, by multiplying each side by 5/4:

20 = 4/5*(requested volume)

If he had used [x = requested volume], instead, then his equation would have been:

(4/5*x - 4) / (4/5*x + 4) = 2/3

Solving this yields x = 25.

PS: We all need to read Denis' posts carefully; he regularly changes symbols already in use. :cool: