Science Fair Ticket Revenue: Kids Vs. Adults

Hey guys! Let's break down a fun little math puzzle about a science fair, focusing on economics and figuring out how many kids and adults showed up based on the ticket prices and the total cash collected. This is a classic word problem that touches on basic algebra, but don't worry, we'll go through it step by step. We'll look at how to approach the problem, the key information we need, and then dive into the solution. This will help you understand the relationship between ticket prices, the number of attendees, and the total revenue generated. So, grab your thinking caps, and let's get started! Understanding this problem is helpful for anyone, whether you're a student, a parent, or just someone who likes to keep their math skills sharp. Ready to unravel the mystery of the science fair attendance?

Understanding the Problem: The Basics

Alright, let's get to it. The core of our problem revolves around a science fair and the money it made from ticket sales. We have two types of tickets: one for children and one for adults. Children's tickets cost 10 rupees each, while adult tickets cost 25 rupees each. The total revenue collected from the ticket sales was 740 rupees, but here's the kicker: this figure only represents 50% of the total income. The main goal is to figure out exactly how many children attended the science fair. To solve this, we'll need to find the total revenue first, and then we'll be able to use the ticket prices and the relationship between the number of children and adults to find our answer. It’s all about setting up equations and using some simple math skills.

So, what kind of things should we remember when dealing with this kind of problem? Think about the importance of breaking down the problem into smaller parts. Also, it is useful to write down everything you know: the ticket prices, the total revenue (from 50%), and the ultimate goal (finding the number of children). This will provide a clearer picture of how to solve the problem. Remember that we need to find the total revenue. Once you have that, you will need to work out how the money was split between the children and adults. The key here is to use the information you have and apply it step by step. Let's get those brains working!

Identifying the Key Information and Setting Up the Equations

Alright, let's dig deeper. To get started, we have to identify the key pieces of information: the ticket prices, the 50% revenue, and what we need to find. We know:

• Child's ticket price: 10 rupees
• Adult's ticket price: 25 rupees
• 50% of the total revenue: 740 rupees

Our goal is to find the number of children who attended the fair. To make this easier, let's introduce some variables. Let:

• c = the number of children
• a = the number of adults

We can set up two equations based on the information we have. First, we need to find the total revenue. If 740 rupees is 50% of the total revenue, then the total revenue (R) can be calculated as:

R = 740 * 2 = 1480 rupees

Now, we know the total revenue is 1480 rupees. Our second equation is based on the total money collected from ticket sales. The money collected from children's tickets (10c) plus the money collected from adult tickets (25a) equals the total revenue:

10c + 25a = 1480

This looks like one equation, but we can use it to find the relationship between children and adults. However, we still don't know how many of them attended the fair, which is what we are trying to find out. To make our math easier, let's consider using guess and check. This method can be really effective when you have some variables to work with. Remember to set up your equations clearly and think through each step. Now we have the information, let’s use it!

Solving for the Number of Children: Step-by-Step

Okay, guys, let's solve this thing! We know the total revenue is 1480 rupees, and our main equation is 10c + 25a = 1480. This can also be simplified by dividing every term by 5, to get 2c + 5a = 296. Now let's use the guess and check strategy. Let's start by guessing the value for a and then working backward to see what c would be. Keep in mind that c and a must be whole numbers because you can't have a fraction of a person.

Guess 1: Assuming a = 10

If a = 10, then the equation becomes:

2c + 5(10) = 296 2c + 50 = 296 2c = 246 c = 123

So, if there were 10 adults, there would be 123 children.

Guess 2: Assuming a = 20

If a = 20, the equation becomes:

2c + 5(20) = 296 2c + 100 = 296 2c = 196 c = 98

So, if there were 20 adults, there would be 98 children.

Guess 3: Assuming a = 30

If a = 30, the equation becomes:

2c + 5(30) = 296 2c + 150 = 296 2c = 146 c = 73

So, if there were 30 adults, there would be 73 children.

Guess 4: Assuming a = 40

If a = 40, the equation becomes:

2c + 5(40) = 296 2c + 200 = 296 2c = 96 c = 48

So, if there were 40 adults, there would be 48 children.

Guess 5: Assuming a = 50

If a = 50, the equation becomes:

2c + 5(50) = 296 2c + 250 = 296 2c = 46 c = 23

So, if there were 50 adults, there would be 23 children.

There are multiple combinations, but we need to consider there is one more information we have to figure out. That is: the total collected income from 50%. Let's calculate the total collected income from 50% of each guesses.

Guess 1: Assuming a = 10 and c = 123

Income = 10 * 123 + 25 * 10 = 1230 + 250 = 1480. 1480 * 50% = 740.

So, if there were 10 adults and 123 children, the income is equal to the original 50%.

So the answer is: There were 123 children among the science fair. It looks like the answer is 123 children and 10 adults. Now we have our answer! Congratulations on solving this problem with me.

Conclusion: Reflecting on the Solution and Key Takeaways

Great job, guys! We have successfully figured out the number of children who attended the science fair. We used our knowledge of ticket prices, revenue, and a bit of algebra to find our answer. To recap, the key steps were identifying the important information, setting up the equations, and solving them systematically. Remember, we had to find the total revenue first, which was crucial. We then created equations to find the relationship between the number of children and adults. Using a guess-and-check approach helped us narrow down possible combinations until we found the perfect fit. These kinds of problems help you think about the relationship between different factors, which is useful in everyday life. So, the next time you see a similar problem, you'll know exactly how to tackle it. Keep practicing, and you'll get better at solving these math puzzles. Stay curious, keep exploring, and thanks for joining me today! I hope you enjoyed this session as much as I did. Until next time, keep those math skills sharp, and don't be afraid to dive into the fascinating world of numbers!