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Problem 58

At a carnival, $\$ 2,914.25$ in receipts were taken at the end of the day. The cost of a child's ticket was $\$ 20.50$ , an adult ticket was $\$ 29.75$ , and a senior citizen ticket was $\$ 15.25$ . There were twice as many senior citizens as adults in attendance, and 20 more children than senior citizens. How many children, adult, and senior citizen tickets were sold?

Answer

without taxes, I spent $\$ 21,$ John spent $\$ 32.50$ and the third roommate spent $\$ 40$, while with taxes I spent $\$ 22.05,$ John spent $\$ 35.10$ and the third roommate spent $\$ 43.60$

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## Discussion

## Video Transcript

All right. So Number 58 a carnival that takes in $2914.25 and receipts on their cell. Three types of tickets. Adult tickets, which we'll call X um, in the cell child tickets. And it's also Sameer Stick. It's and so will define X. Y and Z is a number of each type of ticket. It's so, um and then they give us two additional pieces of information here. One is that twice There's twice as many seniors. It's adults, and they're 20 more children as seniors. Okay, so, um, let's start out by writing out the receipt equation. Okay, So that's money here is made up of money collected from these three types of tickets. So 29. 75. Thanks. Worse. 20 ft. What? Waas 15 25. See, equals $2940. Total sense. Okay, The next one is There's twice as many seniors as adults. Okay, so that means the, um the, uh, press minutes either. So the adults equal half deceivers. We also know that they're 20 more children as C James. Okay, So that means that the children are 20 more children than there's 20 less seniors. So, um, the children, people, seniors plus 20. And so what we want to do then, is used the Memphis substitution to solve this. So what we'll do is we're gonna take these eyes, substitute them into this equations of perspiration, then becomes 29 75 times Z over too. One happened. See how you want. Think about it. Plus 2050 times Z post one plus 15. 25 z equals 29 40 25. All right, so let's go ahead and simplify this. All right, So for the 1st 1 we want to do 29. 75 Bye bye to 48. 75 plus 2050. Easy. Um, Waas. See? 20 times 20 410. And then plus it's you 25 z. Okay, then collect like terms and was attract this 410 over to the other side. So 29 14 cheating. Bye. Minus or 10. It was his 25. All four on your side. 0.25 this side. We have to add 14.875 waas for me. 1 50 plus 15.25. Yeah. When we get 51. 65 z. Was that so? Then I need to do 25 4 25 divided by 50 1 65 And I get approximately. What do you know? I will say two or divided by 50162 Hey, get 49 146 Which doesn't really make sense, but this is roll with it. Um See. Equals, um was 49.47 almost 50 um, accidents. Half of that be about 24.73 and then Z would be 20 more widely, 20 more disease. 69 1 47 All right.

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