Eu number 32. The posted weight limit for a covered wooden bridge in Pennsylvania is 6000 pounds. A delivery truck that is carrying x identical boxes, each weighing 14 pounds will pass over the bridge is the combined the combined weight of the empty delivery truck and its drivers 4500 pounds. What is the maximum possible value for x that will keep the combined weight of the truck driver and boxes below the bridges? posted weight limit? Jeez, all right.

This is a word problem, my friend. Whenever you see a word problem, one thing should run through your head. You want to translate the word problem into an equation into some kind of relationship that you can work with. Okay? And when you're doing this, you want to do it sequentially meaning go through every bit of the word problem. Let's see what relationship you can get.

Alright, so the first sentence Just tell me That the maximum is 6000 pounds. Cool, thank you a second sentence a delivery truck that is carrying extra medical boxes each weighing 14 pounds will pass over the bridge. So Well I can tell you that the total number of pounds of boxes is 14 x right? Because we have X number of boxes and each box weighs 14 pounds so the total weight of all the boxes will be 14 x so that's the first thing on the right now continued if the combined weight of the empty truck or empty livery truck and as drivers 4500 pounds, so I just have another relationship is those two combined will give me 4500 what is the maximum possible value for x that will keep the combined weight of the truck all that posted weight limit below the weight limit. So words like below, words like maximum, those should light up something in your head.

I don't know what that is, but whatever it is for you. It should be That you're going to set up some kind of inequality. It's really simple. Don't let inequalities ruin your day. They certainly have not ruined my day. Ever since I stopped letting them ruin my day.

You feel me? I know you. Okay? So the way we're going to write this is all right, well, the total, the total total total, the combined weight of the truck, the driver, and the boxes has to be below this weight limit. So let's add up what the truck driver and box is going to equal to. So that's going to be the truck and driver together.

They're 4500 plus the weight of all the boxes. Well, that we said that's 14 x, right? Each box weighs 14 pounds, and we have four and we have X number of those boxes. So that's 14 X. Those have to be below. Here's my X, did it Forget about it.

All of that weight has to be below the weight limit, which is 6000. And what are they asking you? They're asking you to to figure out the possible value of x, that will give you the maximum the maximum value. So any maximum number of boxes that you can have where you can still be under 6000? Well, you just got to solve for x men. That's all they're asking.

And again, don't let this this weird looking thing here here, a triangle missing inside the inequality. Let you get this weighted from this question. It's just like anything else. So if you want to solve for x what was so surprising 4500 from each side that'll give you 14, x is less than 1500. Let's divide by 14. We didn't dissipation is grown.

We get x is less than what do you think? Well, just crunch don't think about it just country your calculator 107 and one seven. But keep in mind, that is not your answer because they asked you for the possible value the maximum possible value of x and x is the number of buyers As you can't have a seventh of a box, right, the number of boxes or x has to be an integer, like 123 54 6000, whatever. Okay, so that means well let's just round that down. So your answer should be 107. That is the maximum since I can't have a seventh of a box, so I'm just gonna round it off at 107