Now that we've learned how to solve inequalities, we're going to look at using inequalities to help us answer word problems. Just like with any type of word problem you're trying to solve, it's a good idea to read it through twice. The first time, read the word problem straight through so that you get a sense of overall what it's talking about and what you're expected to do. And then the second time, read one part of the word problem at a time to try to pull out the key information that you need to help you set up an equation, or in this case, an inequality. So for our first word problem, we have an elevator can hold at most 1080 kg. Each person on the elevator weighs 90 kg on average. Write and solve inequality to show the maximum number of people that the elevator can hold. So here we see we have a situation where we want to figure out how many people an elevator can hold and they tell us the weight that it can hold at most. We see here in the first sentence it says an elevator can hold at most 1080 kg. So let's see if we can take that and help us start to set up our inequality. We can write that as the total weight of the people is less than or equal to 1080. Now we also know that each person on the elevator weighs 90 kg on average. So that means that the total weight of the people will be 90 kg times however many people you have. So we could write it like this, 90 times the number of people. And now we know that altogether that total has to be equal to or less than 1080. Now, you can see here we actually do have an inequality set up, but usually when we're writing equations and inequalities, we don't use words, we can use variables for anything that we don't have a number to plug in for. So instead of having number of people, let's just use the variable n. So we can rewrite this as 90 times n is less than or equal to 1080. Now we have an inequality set up for us that we can solve for n. So on the left side we have 90 times n. We'll get n by itself, by dividing by 90. Do the same thing on the right side, the 90s will cancel out, leaving us with just n. And on the right side, 1080 divided by 90 leaves us with twelve, brings down the inequality symbol, it stays the same because we divide it by a positive number. So now our solution is n is less than or equal to twelve. And since n represents the number of people, we could say that the number of people has to be less than or equal to twelve. Or if we use the words from the word problem, we would say the elevator can hold a maximum of twelve people. Let's look at one more example. A school football team is washing cars to raise money. They need a total of at least $270. They already have $95. Write and solve an inequality to show the minimum amount of additional money needed to meet their goal. So here we can see that football team wants to raise some money and they need at least $270. They already have some of the money, but we need to figure out how much they need an additional money in order to hit that goal so they need at least $270. If we write that out as an inequality, we could say that the total money needed is greater than or equal to $270. We also know that they already have $95. So if that total money needed, they have 95 of it. But they also need additional money. So we could write that as the total money needed breaks down into 95 plus the additional money that they need. And we know that altogether that has to be greater than or equal to 270. Now, instead of using the words additional money needed in our inequality, we can use a variable like M. So if we write that over, we'll have 95 plus m is greater than or equal to 270. Now let's solve this inequality. On the left side, we can subtract 95 to get M by itself. We'll do the same thing. On the right side, 95 -95 will cancel out. So we'll have just M left and on the right side 270 -95 leaves us with 175 and we'll bring down our inequality sign. Since we only subtracted 95, our inequality does not change. So now we have that m is greater than or equal to 175. So that means the additional money they need has to be greater than or equal to $175. Or we could say it as the team needs a minimum of $175 of additional money.