Systems of Inequalities Graph the solutions set of the system if inequalities. Find the coordinates of all vertices, and determine whether the solution set is bounded.
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College Algebra
- Height and Weight For a healthy person who is 4 feet 10 inches tall, the recommended minimum weight is about 91 pounds and increases by about 3.6 pounds for each additional inch of height. The recommended maximum weight is about 115 pounds and increases by about 4.5 pounds for each additional inch of height. (a) Let x be the number of inches by which a person’s height exceeds 4 feet 10 inches and let y be the person’s weight (in pounds). Write a system of inequalities that describes the possible values of x and y for a healthy person. (b) Use a graphing utility to graph the system of inequalities from part (a). (c) What is the recommended weight range for a healthy person who is 6 feet tall?arrow_forwardShanthie needs to earn at least $500 a week during her summer break to pay for college. She works two jobs. One as a swimming instructor that pays $10an hour and the other as an intern in a law office for$25 hour. How many hours does Shanthie need to work at each job to earn at least $500 per week? (a) Let x be the number of hours she works teaching swimming and let y be the number of hours she worksas an intern. Write an inequality that would model thissituation. (b) Graph the inequality. (c) Find three ordered pairs (x,y) that would be solutions to the inequality. Then, explain what that means for Shanthie.arrow_forwardElena 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 that pays $9 an 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? (a) 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 that would model this situation. (b) Graph the inequality. (c) Find three ordered pairs (x, y) that would be solutions to the inequality. Then, explain what that means for Elena.arrow_forward
- Physical Fitness Facility A physical fitness facility is constructing an indoor running track with space for exercise equipment inside the track (see figure). The track must be at least 125 meters long, and the exercise space must have an area of at least 500 square meters. (a) Write and graph a system of inequalities that describes the requirements of the facility. (b) Find two solutions of the system and interpret their meanings in the context of the problem.arrow_forwardArmando’s workouts consist of kickboxing and swimming. While kickboxing, he burns 10 calories per minute and he burns 7 calories a minute while swimming. He wants to burn 600 calories each day. (a) If x is the number of minutes that Armando will kickbox and y is the number minutes he will swim, find the inequality that will help Armando create a workout for today. (b) Graph the inequality. (c) List three solutions to the inequality. What options do the solutions provide Armando?arrow_forwardApplications Fundraising A college club is selling baskets of fruit and blocks of cheese to raise at least 600 for a local childrens hospital. a. If the profit for selling a basket of fruit is 5 and for selling a block of cheese 6, write a system of inequalities that describes when x boxes of fruit and y blocks of cheese will cause the fundraising goal to be reached. Hint: Remember that a negative number of baskets of fruit or blocks of cheese cannot be sold. b. Graph the system of inequalities.arrow_forward
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