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).