Newmovies charge $4 each month to use their dvd rental service and $2.25 per dvd

Step-by-step explanation:

Let's look at a few examples where we know the number of movies.  Let's say  just 1 movie is rented.  Well, then there's the subscription charge of 4 dollars and then 2.25 for the one movie.  Two movies would be 4+2.25+2.25.  3 would be 4+2.25+2.25+2.25.  So the number of 2.25s increases with each movie.  You could brute force it and just keep adding 2.25 until you get 31, but there's a better way.  

Multiple additions like this is of course multiplication.  so one movie is 1*2.25, two is 2*2.25 and so onwe want to know how many were bought, so let's call that number something we don't know, x.  Also, you want to take into account the 4 dollar subscription fee.  This leaves us with an equation that looks like this.

4+2.25x = 31

Now, to solve for x we can do a few things to this.  I'm assuming you are new to this so I will take it slow.  Let's say it was a simpler problem.  5+x=10.  Or five plus something equals 10.  You might be able to figure it out super easily and just know that 5+5 is 10.  A way to solve it with our problem though is to take the euations 5+x=10 and manipulate it on each side of the equation.  Here, 5 is being added to x, but what if we subtract 5?  well, 5+x-5=x.  Since we did that to one side of the equation though we have to do the ame to the other side.  so 10-5.  Or in other words we subtracte 5 from both sides.

5+x=10

-5      -5

x = 5

So that's ne part of how we are going to find x in 4+2.25x = 31

4+2.25x = 31

-4               -4

2.25x = 27

Now, in the last part 5 was being added so we subtracted.  Here, 2.25 is being multiplied so we divide.  If we divide both sides by 2.25 we get x = 12, so that's the answer.

the 2 1/2 for $6.25

Step-by-step explanation:

convert the fractions to decimals and divide. the lowest number is the best buy because you spend less