Capacity

[Guest]

Three containers of different sizes can be filled with a quantity of water. The small container can be filled 4 times, or the medium 3 times with 2 gallons remaining, or the large 2 times with 4 gallons remaining.

Determine capacity of each container.

Let S = Small container
Let M = Medium container
Let L = Large container

How do I proceed ?

[Guest]

Why in all these questions do You just simply list at random, items from the question and give them a Letter and not do anything else with it.

You do not apply any logic or indication of reasonable thinking....

That does not add anything to the question or do anything to provide a solution.....

This question is very similar to the gunpowder Question posted earlier....
..............

First of all you need to read the question....and the gunpowder question

Then work out logically what the question is telling you and what it wants you to find.

1....The question tells you there is a quantity of water.....It does not tell you how much.
2....The question tells you there are 3 containers of different sizes and they can be filled with a quantity of water.
3....The question tells you the relative size of each container and how they relate in size to the quantity of water.
4....The question tells you how many times a container can be filled and how much water remains.
5....The question only mentions a quantity of water, so the amount of water in each test fill will be the same....

6....You are asked to find the capacity of each container...

Now you can Let S = small container, M = medium container, and L = Large container and setup equations of each test filling exercise from the information given in the question. And we will also Let Q = the quantity of water.

So for each test......

Small....... 4S = Q = the quantity of water

Medium...... 3M + 2 = Q the quantity of water

Large....... 2L + 4 = Q the quantity of water

Now we can rearrange these to give the size of each container in terms of Q.....

Small..... S = Q/4

Medium.... M = (Q - 2)/3

Large..... L = (Q - 4)/2

These all added together add up to the quantity of water because we are told the 3 containers can be filled with a quantity of water...this is what we let equal Q.

Q = S + M + L

Q = (Q/4) + (Q - 2)/3 + (Q - 4)/2 ....take LCM = 12 change all to 12ths

Q = (3Q/12) + (4Q - /12 + (6Q - 24)/12

Q = (13Q - 32)/12

12Q = 13Q - 32

13Q - 12Q = 32

Q = 32 gallons ....total quantity of water

S = 32/4 = 8 gallons

M = (32 - 2)/3 = 10 gallons

L = (32 - 4)/2 = 14 gallons

[Guest]

Q = (3Q/12) + (4Q - /12 + (6Q - 24)/12

In the last post this line showed a smiley in it...due to some error ?????

It should read

Q = (3Q/12) + (4Q - /12 + (6Q - 24)/12

hope it reads OK this time.....??????

[Guest]

I don't know what is happening......

on my computer it still shows a smiley

where the smiley is it should be -8 ....minus 8

(4Q - /12