Now we're going to continue looking at how we can set up inequalities to help us solve word problems. And the ones that we're going to look at today will be two-step inequalities. And just like with any type of word problem, you want to read it through twice. So we're going to read it through first to make sure that we understand what the problem is about. And then we'll read it through a second time to look for specific information that will help us to set up our inequality so we can solve it and answer the question. So here's our first word problem. Jerry has $17.50 and is going to the movie theater. A movie ticket costs $10 and snacks are $2.50 each. What is the maximum number of snacks she can buy? So, looking at the first sentence, it says Jerry has $17.50. So that means that that's the most that she can spend. So all of the money for the ticket cost and the snacks have to be less than or even equal to $17.0.50. She just can't go over that amount. So we can set that up as the cost of the tickets and the snacks is less than or equal to $17. We're also told that the movie ticket costs $10 and snacks are $2.50 each. So we can break down the cost of the ticket and snacks using that information. The ticket is $10. And then for the snacks, it says that they're $2.50 each. So to find the total cost of the snacks, we'd have to multiply $2.50 times whatever number of snacks she decides to buy. And we don't know how many snacks she's going to buy, so we don't have a number to put in for that. We'll just leave it as words. But we do know that all of that, all the total for the tickets and the snacks has to be less than $17.50. So we really do have an inequality already set up here. Ten plus 2.50 times whatever number of snacks she buys is less than or equal to 17.50. But we normally don't solve inequalities when they're set up like this. So let's clean this up a little bit. Instead of writing number of snacks, let's use a variable like n. So we can write this over as ten plus 2.50 times n is less than or equal to 17.50. And now we can solve our inequality. So let's focus on the left side where our variable n is, so we can get n by itself. First we'll subtract ten, do that on both sides and we'll see what we're left with. Ten minus ten will cancel out. So on the left we'll just have the 2.50 times n, and on the right we have 17.50 minus ten. That would leave us with 7.50 on that side. So if we bring that all down, we have 2.50 times n is less than or equal to 7.50. Now to get n by itself, we'll need to divide by 2.50, do the same thing on the other side, 2.50 over 2.50 will cancel out. So on that side I'll just have n left. On the right side, 7.50 divided by 2.50 will equal three. So that becomes n as less than or equal to three. So that's our solution is that n, which represents the number of snacks, is less than or equal to three. Or to put it in terms of the word problem, we could say that Jerry can buy a maximum of three snacks. Let's look at one more example. The length of a rectangle is 3 CM more than its width. The perimeter is less than 38 CM. Write and solvent in any quality to find possible values of the width. So we know that we have a rectangle and there's some information about the length and the width and even the perimeter of the rectangle. Well, to help us picture what's going on, let's draw a rectangle and let's label one side as the width, and the other direction we can label as the length. Now let's look at the word problem to see what other information we can find. So it says the length of the rectangle is 3 CM more than the width, but we don't know what the width is. So we'll use a variable. Let's use w to label the width, and the length is 3 CM more than the width. So that means that we can write the length as w plus three to represent the three more centimeters. We're also told that the perimeter is less than 38 CM. So let's write that as an inequality and we can just use the word perimeter with the less than sign and 38. Now let's think about what we know about perimeter. We know that the perimeter has to be the sum of all the sides of the rectangle. Basically, if we add the length of all of the sides, that will equal the perimeter. So if the left side of the rectangle is represented with W, then the side across from it also has to be that same measurement, whatever W is. And if the bottom side is w plus three, then the side across from it at the top has to also be the same measurement. So we can label that as w plus three. Now, if we add all those sides together, that's equal to the perimeter. So let's break the perimeter down into the sum of all those sides. So we have the left side as w, we'll add the bottom side, which is w plus three, add the right side, which is w, and the top side as w plus three. So we have all of that being added together, and that total of the perimeter is less than 38. Now we have a bunch of w's in there and a couple of threes. So we can definitely combine like terms to simplify this inequality. And if we do that it will simplify to four W plus six. We have the four W's there, and three plus three gives us six, and that is less than 38. So now we have an inequality that's much clearer to work with and we can solve for W. So we can subtract six from both sides. The six minus six will cancel out. So on the left we'll just have four W, and on the right, 38 minus six will leave us with 32. So this becomes four W is less than 32, and then divide by four on both sides, four over four will cancel out, and on the right side we have 4. 32 divided by four, which is eight. So this becomes W is less than eight. So our inequality is solved. We know that the width has to be less than eight, and if we write it out as a sentence, we would say the width of the rectangle is less than 8 CM.