Section 2.7 Linear Inequalities in One Variable 175 5c. The cost to rent a banquet facility for a wedding reception is $1500 plus $35 per person for the food. What is the number of attendees the couple can have at the reception if they have at most $5000 budgeted for the reception? Solution 5c. What is unknown? The number of attendees is unknown. Let x represent the number of people attending the reception. What is known? The cost of the reception is $1500 plus $35 per person or 1500 + 35x. The cost is at most $5000. 1500 + 35x ≤ 5000 1500 + 35x - 1500 ≤ 5000 - 1500 35x ≤ 3500 35x 35 ≤ 3500 35 Express statement mathematically. “at most” is ≤. Subtract 1500 from each side. Simplify. Divide each side by 35. x ≤ 100 Simplify. The couple can have at most 100 people attending their reception to have a cost of no more than $5000. Student Check 5 Write an inequality that models each situation. Solve the inequality and answer the question in a complete sentence. a. Darryl has scores of 90, 85, 83, and 92 on his first four tests in his math class. What score does he need on the fifth test to have a test average of at least a 90? b. Rosita’s final grade in her math class is based on a weighted average. The weights are as follows: Homework average 10% Test average 45% Quiz average 15% Final exam 30% If Rosita’s homework average is 100, her quiz average is 75, and her test average is 80, what does she need on her final exam to have a final grade of at least 70 in the class? a final grade of at least 80 in the class? c. The cost of the Verizon Wireless Nationwide Select 450 is $59.99 per month. The plan includes 450 anytime minutes and unlimited text, picture, video and instant messaging to anyone on any network in the United States. Additional anytime minutes cost $0.45 each. How many additional minutes can Lisa talk so that her total monthly cell phone bill is at most $75? Round to the nearest minute. (Source: www.myrateplan.com) Troubleshooting Common Errors Some common errors associated with linear inequalities are shown next. �� ������������������������ ������������������ A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 6a. Write the interval for the graph. –5 –4 –3 –2 –1 0 1 2 3 4 5 Objective 6 ▶ Troubleshoot common errors.
hendricks_beginning_algebra_1e_ch1_3
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