How to Calculate Dry Clay and Left-Over Mud for a New Mixture

[jetteichert]

1. You have a quantity of drilling mud left over from a previous job. The mud contains 30% clay and 70% water. Your next job needs a mud with 40% clay and 60% water. How much dry clay needs to be mixed with some of the left-over mud to produce nine tons of a new mixture containing 45% clay? How much of the left-over mixture is used for the new batch?



2. None



3. An excel sheet I worked out, but it solves knowing the quantity of left over mud (user input). Sometimes it helps me think when I work anything.

Okay I am not looking for an answer to this problem (I changed the % and weight anyway). I am actually looking for a second opinion on this problem. To me it is impossible to solve without knowing the amount of left over mud, does anyone else disagree or agree?

My professor seems to give problems that are way to easy or are lacking information unless you have taken higher classes then what I am in (luckily I procrastinated this basic class).

 

[CompuChip]

The mathematician's trick is to give your unknowns names, and express all relations between them as equations.

In this case, I suggest letting x be the quantity (in tons) of left-over mud that you are using and y the amount of dry clay that you add.
Those are two unknowns, so you will need two relations between them. Those could be equations for the total amount x + y, and for the amount of clay. Does that help you taking a shot at it?

 

[Redbelly98]

Moderator's note: the OP has informed the Mentors that s/he has solved the problem.

 

[CompuChip]

In that case, for future reference, let me write down the two equations that I had in mind.

The first one expresses the total weight of 9 tons,
x + y = 9.

The percentage of clay should be equal to
0.30x + y = 0.40(x + y) = 9 . 0.40
(or 0.45, the OP is not really consistent here).

This gives two equations which can be solved for x and y, giving x = 54/7 and y = 9/7 (i.e. you should mix about 7.7 tons of old mud with 1.3 tons of dry clay).

 

[DeeNos]

I would approach this problem by first calculating the total weight of the left-over mud. Since we know that the mud contains 30% clay and 70% water, we can use this information to determine the weight of clay and water in the left-over mud.

Using the given percentages, we can set up the following equations:

Let x = total weight of left-over mud
0.3x = weight of clay in left-over mud
0.7x = weight of water in left-over mud

Next, we can calculate the weight of dry clay and water needed for the new mixture. Since we need a total of nine tons of the new mixture and it contains 45% clay and 55% water, we can set up the following equations:

Let y = weight of dry clay needed
0.45(9 tons) = 4.05 tons = weight of clay in new mixture
0.55(9 tons) = 4.95 tons = weight of water in new mixture

Now, we can set up an equation using the weight of clay in the left-over mud and the weight of dry clay needed for the new mixture:

0.3x + y = 4.05

Solving for y, we get y = 4.05 - 0.3x

To determine the amount of left-over mixture that needs to be used, we can set up an equation using the weight of water in the left-over mud and the weight of water needed for the new mixture:

0.7x + 4.95 = total weight of left-over mud + weight of water needed for new mixture

Since we know that the total weight of left-over mud is x, we can substitute this into the equation and solve for x. This will give us the total weight of the left-over mud, which we can then use to determine the amount of left-over mixture needed for the new batch.

In summary, to calculate the dry clay and left-over mud for a new mixture, we need to first determine the total weight of the left-over mud. Then, we can use this information to calculate the weight of dry clay and water needed for the new mixture. Finally, we can use the weight of water in the left-over mud to determine the amount of left-over mixture needed for the new batch. Without knowing the amount of left-over mud, it would be impossible to accurately calculate the dry clay and left-over mud