At a raffle, 120 tickets are sold at $1 each for two prizes of $30, and $15 suppose you buy a ticket

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Ticket problems are word problems similar to coin problems and stamp problems as tickets may be denominated in specific values.

Be careful to distinguish between the value of the items and the quantity of the items.

A table can be useful for distinguishing between quantity and value in this type of word problems.

Example:
The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?

Solution:
Step 1: Set up a table with quantity and value.

Step 2: Fill in the table with information from the question.

The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?

Let x = number of $3 tickets Let y = number of $2 tickets Total = quantity × value

Step 3: Add down each column to get the equations

x + y = 350                    (equation 1)
3x + 2y = 950                (equation 2)

Use Substitution Method
Isolate variable x in equation 1

x = 350 – y                     (equation 3)

Substitute equation 3 into equation 2

3(350 – y) + 2y = 950 1050 – 3y + 2y = 950 3y – 2y = 1050 – 950

y = 100

Substitute y = 100 into equation 1

x + 100 = 350
x = 250

Answer: 250 $3 tickets and 100 $2 tickets were sold.

Ticket Word Problems

Example:
Jim sold 120 tickets to a game. Adult tickets are $24 each and children tickets are $13 each. Sales are $2110. How many of each was sold?

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Word Problems With Theater Attendance

Example:
500 people see a play. Children are charged $15 and adults $25. Ticket proceeds are $11,250. How many children attended the play?

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Algebra - Word Problems: With Movie Tickets

Example:
For a theater showing 202 tickets were sold. A child’s ticket costs $6.00 and an adult’s ticket costs $10.00. How many tickets of each were sold if the receipts totaled $1708.00?

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Solve Ticket Word Problems In Three Variables

Example:
The Goonies sold 785 concert tickets for a total of $17,650. If good tickets cost $40 and cheap tickets cost $15, how many of each type of ticket did they sell?

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Example:
At the arcade, Sammy won two blue tickets, 1 yellow ticket and 3 red tickets for a total of 1,500 points. Jamal won 1 blue, 2 yellow and 2 red for 1225 points. Yvonne won 2 blue, 3 yellow and 1 red for 1200 points. How much is each ticket worth?

Word Problem - Mixture Of Ticket Sales

Example:
For opening night 328 tickets were sold. Students paid $2 each while non-students paid $4 each. If a total of $910 were collected, how many students and how many non-students attended?

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Ata raffle; 120 tickets are sold at $1 each for two prizes of $30,and $15. Suppose you buy a ticket _ What is the expected gain? [Select ] What is the variance? Select

You buy a lottery ticket to a lottery that costs $\$ 10$ per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $\$ 500$ prize, two $\$ 100$ prizes, and four $\$ 25$ prizes. Find your expected gain or loss.

Okay, So here is the important bit is knowing the difference between a permutation and a combination for winning lottery ticket order does not matter. So we want a combination right, which is gonna be equal in two, and that she's our Where is the total number of objects in the satin for us? This is the 50 possible numbers and our is three number we're choosing. Okay, So it's gonna give us and if factorial over r factorial times and minus R editorial. Okay, this isn't that probability of the number of favorable outcomes over the number of possible outcomes is going to give us the probability that we would win. Okay, so this is to be equal to There's one favorable outcome, which is where all six numbers are correct and the possible outcomes we determine here by doing a combination case. That's gonna be a combination where n is 50 50 possible members to choose from. And then we're choosing these six correct ones. Okay, so this isn't the be equal to six factorial times 50 minus six factorial over 50. Factorial can of you calculate that out. It ends up being one over 15 million. 890,000 and 700. Okay, so they want to use the compliment rule to see that a probability of a loss is going to be equal to one minus the probability of winning, which is going to be equal to one minus this fraction. Here, so is the one over 15 million, 890,000 and 700. Your neck is this. 15 million 890,000 and 699 over 15 million. 890,000 and 700. Okay, so then we get to go into figuring out some he's expected values. Here. I'm gonna start a new page. No, we win. Regained 10 million. But we lose the cost of the $1 lottery ticket rights. When we win, we're actually getting nine million 999,000 and $999 profit. When we lose, we lose $1. That is the cost of the lottery ticket. So then the expected value Is it me the sum of each possibility with his probability, right? So the expected value, then it's going to be equal to what we would get if we win. So that's nine 1,000,000 999,000 999 times the probability of winning, which was the one over 15 1,000,008 100 90,000 and 700. We're gonna add that to If we lose, that gonna be a negative one for the $1 loss. We're gonna multiply that then by the probability that we lose And that was the 15,000,800. Sorry. If we go back to the first Patriots. See that? Probably if we lose here. Is this 150 90,600 99 Over 15 million 890,000 700. No one's to you. But this interior calculator, it'll reduce down to negative 37 cents. So the expected value of each lottery ticket is a 37 cent loss.

So we know from the first ticket That it costs you $3 to play the game. And if X. Is the random variable of how much money you can net. Then if it's $1,000 ticket, you met 997 and there's a one out of 1000 chance of that happening. And if you get the $500 prize then you net for 97. And again there's only one ticket out of 1000 that has that. And then if you get the $100 prize, you're going to only net 97 and there were five of those tickets. So the most likely thing to happen was that you just lose your $3 and you have a 993 out of 1000 chance. And so in the previous question number 15, we find what the expected value of X is By taking that 997 times the one over 1000 plus the 4 97 times the one over 1000 And so on. The 97 over times the five over 1000 and the negative three times. So we're basically doing question 15 and 16. And when we do this, we end up getting negative one. So that's what we expect to happen if you play the game once. Well, what happens if you have a new random variable and you think of playing the game once and also playing the game again and find out what's going to end up happening. And so what is the expected value if you play the game twice? Well, the first time you play the game, you expect To have a certain earning plus the second time you play the game you expect to have the earning and so you're going to have negative one and negative one. You would expect to lose $2. All right. So that's what your expected value would be. So we'll find that when we have a random variable, that is the sum of two random variables that we do simply just add the mean of each one separately to find that. So we would expect if you play twice, you're going to lose on the average $2.

This time they ask us a raffle his hair again. Where the grand prize winner wins $400. Remember, it costs $2. Teoh play this game according to the prom. So but lucky one and people in $388. Um, the three runner ups. Whoa! In $80. But you need to subtract the $2 they spent the seven and then maybe one of the three and 500 people. And now you name and anything just spent. $2 alone will be for 96 out of 500 people and the expected playoff bound of such a player. And that Kim, Well, it'll be negative. 0.72 Not a fair game, and they're at a loss.

Karen is probably playing a game with a deck of cards and they were wanting to find the expected value for this team. Now generally of X. Is equal to the sum of all the excess times the probability of each facts, people, the sum of X times the probability of lecture. So we need to take each situation separately. Now a person is paid $15 for a jack or queen And so we win $15 for jack or a queen. There's a total of 52 cards in our deck And there are a total of eight jacks or queens. So this is acts times probability backs 15 times 8/52. Now we made $5 for drawing a king or an ace. That means we make $5 for kinase. There are eight kings and aces Out of a total of 52 and 20. And then to Epstein's of probability events. Yeah. Now a person who has any other card pays $4. So this means that we're gonna lose $4. That's in a uniform, We've already taken into account 16 cards. And so that means there's 36, we haven't taken into account, So there's 36 ways to lose. And so this is how we're going to find are expected value. There is by adding up these to get And when we do that, that gives us 4/13 for all of this year. And so expected value is four over $13.

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