In Straws We Trussed

Symbols

The first thing we need to know when solving this is what each of our symbols stands for.

Our three symbols are +, =, and *.
+ stands for addition, such as in the simple equation 2+3=5
= stands for equal to, which is found in most simple equations, such as the one above.
* stands for multiplication, such as in the simple equation 2*3=6. In some places, we find that the symbol "x" is used for multiplication, though we will use "*" in our example.

Order of Operations

To be able to solve this equation, we also have to know what the order of operations are. In any equation, we first solve the section found in parentheses, then the exponents, followed by multiplication and division, and finally addition and subtraction. A common way to remember this is by the following acronym:

P	E	M	D	A	S
a	x	u	i	d	u
r	p	l	v	d	b
e	o	t	i	i	t
n	n	i	s	t	r
t	e	p	i	i	a
h	n	l	o	o	c
s	t	i	n	n	t
e	s	c			i
s		a			o
		t			n
		i
		o
		n

Let's start with something easier before we attempt to solve the problem that we were given. Solve this:

2*3+4=?

First, we would follow the order of operation, as expressed by PEMDAS. There are not any parentheses in this equation, just like there are not any exponents. So, we can skip to the MD for multiplication and division. First, we would do the 2*3, which is equal to 6. Then, our equation becomes:

6+4=?

Then, we're left with the last step of PEMDAS, which is addition and subtraction, where we get our answer to be 10.

Here's something a little more difficult:

Here, we first begin with the parentheses, even though it is addition. Our equation becomes

3*12-4*5=?

Still moving from left to right, we then realize that there are no exponents in this equation. So, we move on to multiplication and division. Our first multiplication problem is then 3*12. We then get

36-4*5=?

Remember that we DO NOT move on to the next step until one step is completed. In this problem, we cannot move on to addition and subtraction yet, because we still have 4*5 left to solve. Our equation then becomes simple arithmetic:

36-20=16

Solving for a Variable

Now that you understand the order of operations, its time to be able to solve our equation in our error message, given to us in the form of

Members + 3 = 2 * Nodes

First, we need to assign the terms "Members" and "Nodes" variable, or alphabetical representations. To make it easy, we'll make Members=M and Nodes=N. Thus, our equation becomes:

M + 3 = 2 * N

To be able able to solve an equation like this, we can only have one variable to try to solve for. This means that we need to have a value for either members or nodes. Since we're trying to decide how many members we need, our constant value will be the number of nodes (N). Using the example which we have constructed, we have 4 nodes (one at each corner of the triangle). So, for N, we can substitute the value 4, which is the number of nodes that we have in our model.

M + 3 = 2 * 4

The next step is to isolate the variable to one side of the equation. In order to do this, we much subtract the value on the same side as the M from both sides of the equation. If this doesn't make sense, follow the steps below.

M + 3 - 3 = 2 * 4 - 3

By doing this, we find that 3-3=0 and the variable M is left alone. Then, the other side of the equation becomes 2*4-3 Our new equation is:

M = 2 * 4 - 3

The Final Solution

Using the order of operations, we find that with 4 nodes, we must have 5 members.