Question

write a system of linear inequalities to represent the situation. less than $270. hour lifequarding. in a given week, she can work at most 19 total hours and answer attempt 1 out of 2 10x + 18y

Explanation:

Step1: Define Variables

Let \( x \) be the number of hours babysitting, \( y \) be the number of hours lifeguarding.

Step2: Total Hours Inequality

Total hours \( \leq 19 \), so \( x + y \leq 19 \).

Step3: Earnings Inequality

Earnings: Babysitting earns \( \$10 \) per hour, lifeguarding \( \$18 \) per hour. Total earnings \( < \$270 \), so \( 10x + 18y < 270 \).

Step4: Non - negative Hours

Hours can't be negative, so \( x \geq 0 \), \( y \geq 0 \).

Answer:

The system of linear inequalities is:
\(

$$\begin{cases} x + y \leq 19 \\ 10x + 18y < 270 \\ x \geq 0 \\ y \geq 0 \end{cases}$$

\)