Lesson 24, Section 4.1 (part 2)Applications of InequalitiesPhrases commonly translated to inequalities:Lesson 24, Section 4.1 (part 2)Applications of InequalitiesPhrases commonly translated to inequalities:Words Sample Sentence Translationis at least Gina is at least 18 years old18gare at most There are at most 12 coinsin his pocket.12ccannot exceed The total value cannotexceed $12.12vmust exceed The car's speed must exceed20 miles per hour20sno more than There can be no more than50 people in the room.50pno less than The nut mix can have noless than 5 cups of almonds.5nis less than Marie's age is less than 2121mis more than The house is more than35500 square feet.35500Ais between The distance is between 50and 200 miles.20050 dExamples:1) Metro Concerts can rent a truck for either $55 with unlimited mileage or $29 plus40¢ per mile. For what mileages would the unlimited mileage plan save money?Let m = numbers of miles12) A long-distance phone call using East Calling costs 10 cents for the first minute and 8 cents for each additional minute. The same call on West Call System cost 15 cents for the first minute and 6 cents for each additional minute. For what length phone calls is East Calling less expensive than West Call System?Let m = number of total minutes3) Musclebound Movers charges $85 plus $40 an hour to move households across town. Champion Movers charges $60 an hour for cross-town moves. For what lengths of time is Champion more expensive?Let h = number of hours for the move4) Brad can be paid for his work in one of two ways shown below as plans A and B.Plan A: $150 a week plus $9 an hourPlan B: $12.50 an hourFor what number of hours a week is plan B better for Brad? Round to the nearest tenth of an hour.Let x = number of hours per week25) An insurance company offers two plans. Under plan A, Ginger would have to paythe first $50 of her medical bills and 20% of all bills after that. Under plan B, she would pay the first $250 of bills, but only 10% of the rest. For what amount of medical bills will plan B save Ginger money? (Assume that her bills will exceed $250.)Let b = total amount of medical bills6) A manufacturing company that makes a type of widget has the following cost and revenue functions for making x widgets.xxRxxC30)(1680000)(When revenue is greater than cost, the company makes a profit. Find the number of widgets that must be made in order for the company to make a
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