https://file.aiquickdraw.com/mathbot/file/17298717240427nf8oknd.jpg

https://file.aiquickdraw.com/mathbot/file/1729871755414z4y7ups7.jpg

Let's break down the problem from the image.

We know the following:
- Tickets for the lower deck cost $42 each.
- Tickets for the upper deck are 75% of the cost of the lower deck tickets, which makes them 0.75 × 42 = $31.5 each.

You are tasked with determining which inequality represents all possible combinations of $ x $, the number of lower deck tickets, and $ y $, the number of upper deck tickets, that someone can buy for **more than** $800.

Let's build the inequality:

The total cost for $ x $ lower deck tickets would be $ 42x $, and the total cost for $ y $ upper deck tickets would be $ 31.5y $. So, the total cost for $ x $ lower deck tickets and $ y $ upper deck tickets is:

\[
42x + 31.5y
\]

Since we want to represent the situation where the total cost is **more than** $800, we have:

\[
42x + 31.5y > 800
\]

Looking at the choices provided in the image:
- Option D, $ 42x + 31.5y > 800 $, is the correct answer because it represents spending more than $800.

Do you need further details or have any questions?

Here are 5 related questions for further practice:
1. If you have $500, how many tickets can you buy if all are for the lower deck?
2. What is the maximum number of upper deck tickets you can buy with $600?
3. How much would it cost to buy 3 lower deck tickets and 4 upper deck tickets?
4. If someone buys 2 upper deck tickets, how much money remains from a $700 budget?
5. Can someone buy 10 lower deck tickets for under $500?

**Tip:** When constructing inequalities, always pay attention to whether the problem asks for "less than" or "more than," as this changes the direction of the inequality.

Which inequality represents all possible combinations of x, the number of tickets for the lower deck, and y, the number of tickets for the upper deck, that someone can buy for more than $800? The lower deck tickets cost $42 each, and the upper deck tickets are 75% of the cost of lower deck tickets.

Learn how to solve an inequality for ticket purchases where lower deck tickets cost $42, and upper deck tickets are 75% of the lower deck price. This problem helps to understand real-life application of inequalities. Suitable for students in Grades 7-9.

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