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In question 5a, the inequality represents the relationship between the number of tickets purchased for the lower deck (denoted as $ x $) and the upper deck (denoted as $ y $), with a total spending limit of $800.

- Lower deck tickets cost $42 each.
- Upper deck tickets are 75% of the cost of lower deck tickets, so they cost $ 0.75 \times 42 = 31.5 $ each.

Thus, the total cost for $ x $ lower deck tickets and $ y $ upper deck tickets must be less than or equal to $800:
\[
42x + 31.5y \leq 800
\]
This matches option **B**.

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For question 5b, to check which combinations satisfy the inequality $ 42x + 31.5y \leq 800 $, we substitute the values from each option:

- **Option A**: $ 42(22) + 31.5(5) = 924 + 157.5 = 1081.5 $ (Exceeds 800)
- **Option B**: $ 42(16) + 31.5(6) = 672 + 189 = 861 $ (Exceeds 800)
- **Option C**: $ 42(8) + 31.5(14) = 336 + 441 = 777 $ (Valid)
- **Option D**: $ 42(10) + 31.5(18) = 420 + 567 = 987 $ (Exceeds 800)

Thus, the correct answer for 5b is **C**.

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Do you need further explanation? Here are 5 related questions:

1. How would the inequality change if the total budget was $900 instead of $800?
2. What would happen if the cost of upper deck tickets was reduced to 50% of the lower deck?
3. Can you create a system of equations to solve for specific numbers of tickets purchased with a known total cost?
4. How would you graph the inequality $ 42x + 31.5y \leq 800 $ on a coordinate plane?
5. What is the maximum number of lower deck tickets someone can buy with $800?

**Tip**: Always check your solutions by plugging values back into the inequality to verify if they satisfy the given conditions.

Baseball fans can buy tickets for seats in the lower deck or upper deck of the stadium. Tickets for the lower deck cost $42 each. Ticket prices for the upper deck are 75% of the cost of tickets for the lower deck. 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 no more than $800? Which of the following can represent a possible combination of the upper deck and lower deck tickets?

Learn how to determine the correct inequality for purchasing lower and upper deck tickets within a $800 budget. The problem explores linear equations and cost analysis, using the formula 42x + 31.5y ≤ 800. Suitable for students in Grades 9-10.

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