Hamilton-Wenham Regional High School Algebra I Name:

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1 Inequalities Directions Working in small groups, write an inequality to model each problem. Then solve and graph your solution. After you complete each section, check your answer with the teacher. Section Version Largest Cat The world record for the heaviest domestic cat is a pound tabby. Let C represent the weight of a domestic cat. Write an inequality for C. Graph the inequality. Viking Ships The longest Viking ship that has been found is not quite 95 feet in length. Let V represent the lengths of known Viking ships. Write an inequality for V. Graph the inequality. 3 Work You earn $8.75 per hour at your job. Write an inequality to show how many full hours h you need to work to save at least $650. Graph the inequality. Mr. Brennan Page of 9

2 Section : Version Melting Point Carbon is the element with the highest melting point, 3550 C.Write an inequality that describes the melting point m (in degrees Celsius) of any other element. Graph the inequality. Groceries At the grocery store, you need to spend $50 or more in two months to win a free turkey. A day before the contest ended, Mike had spent $3. Let x represent the amount of money Mike needs to spend to win the free turkey. Write an inequality for x. What is the least amount of money Mike has to spend? Graph the inequality 3 Marathon Paul ran a 6 /5 mile marathon in ¾ hours. Write an inequality to describe the average speeds s of runners who were faster than Paul. Graph the inequality. Mr. Brennan Page of 9

3 Section 4 Version Hourly Wages The hourly wages at a local business are between $8.60 and $4.80 depending upon the job. Write an absolute value inequality describing the possible hourly wages of the employees. Attendance The attendance at home basketball games has ranged between 80 and 540 spectators. Write an absolute value inequality describing the possible attendance at home basketball games. Section 4 Versions Mr. Brennan Page 3 of 9

4 Section 3 Version Mr. Brennan Page 4 of 9

5 Section 3 Version Mr. Brennan Page 5 of 9

6 Section Version Ans: 997 Ans: 5x > 4; x > Long-Distance Services One long-distance telephone company offers a plan such that the first 0 minutes costs $.99 and each additional minute costs $.09. Solve an inequality to find the maximum amount of full minutes you can talk for $5.00. Ans: 64 minutes Mr. Brennan Page 6 of 9

7 Section : Version Ans: 7 months 3 Long-Distance Services One long-distance telephone company offers a plan such that the first 0 minutes costs $.99 and each additional minute costs $.09. Solve an inequality to find the maximum amount of full minutes you can talk for $5.00. Ans: 64 minutes Mr. Brennan Page 7 of 9

8 Section 5 ( version only) Math Club No more than 65 freshmen and sophomores may participate in the math club. There are three times as many freshmen as sophomores. Let x represent the number of freshmen. Let y represent the number of sophomores. Write and graph an inequality that describes the different number of freshmen and sophomores in the math club. Ans: Calculators A store carries $3000 worth of various types of calculators. A scientific calculator costs $0 and a graphing calculator costs $80. Let x represent the number of scientific calculators in stock. Let y represent the number of graphing calculators in stock. Write and graph the inequality that describes the different number of scientific and graphing calculators in stock. Ans: 3 Breakfast You and your friends go to a bagel shop for breakfast. Together you have $ to spend. Each bagel costs $.35 and each glass of juice costs $.80. Let x represent the number of bagels you can buy. Let y represent the number of juices you can buy. Write an inequality that represents the number of bagels x and the number of juices y that your group can afford. Sketch a graph of the inequality. Ans: Mr. Brennan Page 8 of 9

9 Mr. Brennan Page 9 of 9