County Symphony is preparing for a special holiday concert....

County Symphony is preparing for a special holiday concert. Fixed costs associated with the concert are as follows. Rental of performance venue Performer compensation In addition, County Symphony must pay a local amusement tax of $7 for each concert ticket sold. The performance venue has seating ca school has offered a flat contribution of $3,500 for 100 tickets for their staff. If County Symphony accepts the offer from the prep school A) It will decrease by $3,000. B) It will decrease by $2,400. C) It will increase by $2,800. D) It will increase by $3,500.

Transcript

00:01 Okay, for this problem, we're looking at some concert receipts and we're looking at some business applications of quadratic problems so let's look at this how much this concert cost.

00:12 So let's just write down what we know now we kind of see the pattern.

00:16 Let's go in here.

00:17 I'm going to write down what we know kind of as an equation because we see if these business applications basically we need to talk about the cost of something and the number of okay, so let's kind of fill in what we have so i'm going to read the problem here that the concert cost $15 and the average attendance has been 1 ,200 % so let's say 1200 is our attendance and the management projects that for each 50 cents increase in price there'll be every 30 % decrease in price 40 more patrons will attend okay so if you lower the cost so we'll have 40 more all right so before i go too far that's my n so let's and people the number of 50 cent price drops.

01:18 All right, so there is the basically the number of people, number of tickets we're going to sell.

01:33 And then the actual cost, it's talked about $15 is the average is the existing cost.

01:43 And we're gonna do a minus sign because they said we're gonna reduce it 50 cents per tickets.

01:49 And we're gonna do that for a certain number of time.

01:51 So that's the number of reductions.

01:53 So the minus here is the cost is going down here a little bit.

01:58 And so we have the product of the number of things we sell times the cost of what we sell.

02:04 And we know overall they want to know how many people need to attend the concert if the receipts were 17 ,280.

02:16 All right.

02:22 So let's be careful at the end because you want to know the number of costs.

02:27 So we're going to get the number of price bumps or price decreases, i should say.

02:31 But we want to know the number of tickets at the end.

02:37 Make sure we make that adjustment at the end.

02:40 All right.

02:40 Let's get to green here, so we need to multiply all these things out.

02:45 So we're going to take 15 times 1 ,200.

02:55 So let's multiply that out first.

03:01 Let's be 18 ,000.

03:02 Yes, we have this here is 18 ,000 out front.

03:08 And then we have 0 .50 times 1, well, 0 .50 is like half.

03:13 1 ,200, so that's 600...

Question

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