Angelina is working with function machines. she has the two machines shown at right. she wants to put them in order so that the output of the first machine becomes the input of the second. she wants to use a beginning input of 6. in what order must she put the machines to get a final output of 5?

We are given two machines in series. The first machine receives an input of 6. We are asked to determine the order of the machines to get a final output of 5. Now, we have to illustrate the problem and arrange the machines in series, input 6 going into the second machine and indicate an output of 5. So we do a balance on machine 2:

In = Out

Input value is 6 and output is 5 plus (the remaining value) x

6 =  5 + x

We need to determine x:

6 = 5 + x 
1 = x

So there should be another output, it could be a waste stream of 1 from machine 2 to balance the system.