Question

midterm review 2025-2026

1. graph the system of inequality \\(\

$$\begin{cases}5x + 2y \\leq 10 \\\\ y > -x + 1\\end{cases}$$

\\) to show the solution set.

1. a beach resort offers two types of lounge chairs for rent: basic and deluxe. the resort owns no more than 50 lounge chairs in total. additionally, the daily revenue from renting basic chairs is $5 per chair, while the revenue from deluxe chairs is $7 per chair. the resort wants to earn more than $300 in daily revenue from chair rentals. write a system of inequalities to represent this situation using \\(b\\) for the number of basic chairs and \\(d\\) for the number of deluxe chairs.
2. write the system of inequalities that represents the solution shown below.

Explanation:

Question 34 Solution:

Step1: Define Variables and Total Chairs

Let \( b \) = number of basic chairs, \( d \) = number of deluxe chairs. Total chairs: \( b + d \leq 50 \) (since "no more than 50").

Step2: Define Revenue Inequality

Revenue from basic: \( 5b \), deluxe: \( 7d \). Total revenue > 300: \( 5b + 7d > 300 \).

Step3: Non - Negative Constraints

Since number of chairs can't be negative: \( b \geq 0 \), \( d \geq 0 \) (though maybe not required, but contextually chairs are non - negative). But the main system from the problem's info is \(

$$\begin{cases}b + d \leq 50\\5b + 7d > 300\\b \geq 0, d \geq 0\end{cases}$$

\), but focusing on the two key inequalities from the problem's description (total chairs and revenue).

Answer:

The system of inequalities is \(

$$\begin{cases}b + d \leq 50\\5b + 7d > 300\end{cases}$$

\) (along with \(b\geq0,d\geq0\) if non - negative is considered, but the core inequalities from the problem's given conditions are these two).