Problem

Truck Mechanics. An engine repair cost a truck ow…

Problem 23 Easy Difficulty

Concerts. The fee to rent a concert hall is $\$ 2,250$ plus $\$ 150$ per hour to pay for the support staff. For how many hours can an orchestra rent the hall and stay within a budget of $\$ 3,300 ?$

Answer

$7 \mathrm{hr}$

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Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 5

Problem Solving

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Video Transcript

okay in question. 45. They asked us about rental rates. It's a student council. Wants to rent a ballroom for the junior prom Bulls. Rental rate is $1500 for three hours, and I got $125 for each additional half an hour. Supposed student council raises $2125. What is the maximum number of hours for which they can run the bull? Okay, so the first thing that we know, it's $1500 for three hours. Okay, So that means that for those 1st 3 hours, Okay, we spend $1500 so it's about $500 per hour. Okay. So that 1500 we could already put in there. So that 1500 gives us three hours. You wanna make sure we keep track of that? So it's approximately well, is $500 an hour? 500 per our. And how did I get that? I did 1500 divided by three. Okay, then it's 125 each additional half hour now, because you want the maximum number of hours. Let's think to ourselves. It's 125 for 1/2. An hour, $125 or half an hour. Then it would be $250 for an hour. Okay, after that. Okay. So initially clothes for three hours and more expensive. And then, um then the more hours it becomes a little bit cheaper, so it's 2 50 2 50 x, and I'm gonna make X the number of ours. Okay, So I didn't use half hours because I figured if I did that and I have that X to be seven, and that means there's 7/2 hours, which is really 3.5 hours, it may become confusing, and I'm we put down the wrong answer, so I made it into ours there. Okay, so it's a supposed to counsel Reeses $2125. What is the maximum number of hours? Which means that the most they can spend is 2120 $5. 2000 $125. Okay. And let me just box this over here, okay? So again, now we're just gonna solve, like we did before. And like we've been doing, we subtract 1500 from both size. We subtract 1500 from both sides. We get 250 x is less than equal to. And now we're gonna get to 1 to 5. Take away 1500 which is 625. We divide by 2 50 on both sides, and we get that axe is less than or equal to. And remember, this is gonna be the, um and I should have made that clear in my left statement. But this is going to be the number off additional additional hours beyond that three that I've already paid for. Okay, So less than or equal to 2.5. Okay, so why not, like, why can't Unless it says in the question the whole number hours, right? We'll see if it does the maximum number of hours which they can run. The bullet doesn't so we could party for an extra half an hour. Okay, so that means we're gonna take that three, okay? And we're gonna add it to our 2.5. So 5.5 hours

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