**Modeling Linear Inequalities with Two Variables** **Problem 278:** Elena needs to earn at least $450 a week during her summer break to pay for college. She works two jobs: one as a swimming instructor at $9 per hour, and the other as an intern in a genetics lab for $22.50 per hour. How many hours does Elena need to work at each job to earn at least $450 per week? 1. Let \( x \) be the number of hours she works teaching swimming, and let \( y \) be the number of hours she works as an intern. Write an inequality to model this situation. 2. Graph the inequality. 3. Find three ordered pairs \((x, y)\) that are solutions to the inequality. Then, explain what these solutions mean for Elena. --- **Problem 280:** Armando's workouts consist of kickboxing and swimming. While kickboxing, he burns 10 calories per minute and 7 calories per minute while swimming. He wants to burn 600 calories each day. 1. If \( x \) is the number of minutes Armando will kickbox and \( y \) is the number of minutes he will swim, find the inequality that will help Armando create a workout plan for today. 2. Graph the inequality. 3. List three solutions to the inequality. What options do these solutions represent for Armando?

Simone earned $500 doing extra chores during the summer. She put some of the money in a CD that earned 5.5%. She put twice as much in a savings account that earned 4.8%. She put the same amount that she put in the savings account into a bond fund that earned 3.7%. After one year, the three accounts made $22.50 in interest. How much did Simone put in the CD?

an artist invests in a mutual fund account paying 8% and $8000 more than three times as much in a mutual fund account paying 6%. her total annual interest income from the investments is $1520. how much does she invest at each rate?

A manager has $4,000 budgeted for raises for four full time and two part time employees. Each full time employee receives the same raise, which is twice the raise that each of the part time employees. What is the amount of raise that each full time employee receives?