Hi again MHF,

I'm a bit confused so any help you can provide is greatly appreciated. Thanks a lot. :-)

"Describe how the jester must place the mystery bags and lead weights so that the equation will be a representation of the situation.

Then find the weight of the mystery bag."

a. 5M + 24 = 51 + 2M

b. 43M + 37 = 56M + 24

c. 12M + 15 = 5M + 62

does M equal the mystery weight of the bag?

From what I understand, yes.

From what I understand, they want you to make M the subject of the equation, or, in other words, find the value of M.

To do this, we need to understand the process of undoing/manipulating equations.

The opposite of Addition is Subtraction
The opposite of Multiplication is Division

Hence, to make M the subject in these equations we need to undo some of the operations and shift a few things around.

a. 5M + 24 = 51 + 2M - The aim is to get the M's onto one side, whilst keeping both sides equal (like keeping weights in balance on a scale).

Let's push M onto the left side, as it's mathematical convention for the subject to appear on the left.

a. 5M + 24 = 51 + 2M

1. Get M onto the left side.
3M + 24 = 51 (We substracted (opposite of addition) 2M from both sides (keeping the equation balanced).)

2. Get M by itself.
3M = 27 (We need to undo the addition of 24 (opposite is substraction) before we can deal with the 3 in front of the M).

- M = 27/3 = 9 (We undid the multiplication on M by dividing both sides by 3 (opposite to the multiplication).

If you understand the process, can you complete the rest by yourself?

Yes, I do understand -- and thanks for your assistance once again