EXERCISES PPractice and Problem Solving

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1 EXERCISES PPractice and Problem Solving For more practice, see Etra Practice. A Practice b Eample Eample (page 78) Is the given ordered pair a solution of the sstem?. (, 9). (, 0). (-, 0) # $ $ 0 # 9 + Solve each sstem b graphing.., + 5., $ 6 - # - # , - 9. # + 7 # $ # 0. $ # $ 9 # $ 0. -, # $ 7 Eample (page 78) Write a sstem of inequalities for each graph Eample (page 79) 0. Budget Suppose ou bu flour and cornmeal in bulk to make flour tortillas and corn tortillas. Flour costs $.50/lb. Cornmeal costs $.50/lb. You want to spend less than $9.50 on flour and cornmeal, and ou need at least lb altogether. a. Write a sstem of inequalities that describes this situation. b. Graph the sstem to show all possible solutions Chapter 7 Sstems of Equations and Inequalities

2 . Suppose ou want to fence a rectangular area for our dog.you will use the house as one of the four sides. Since the house is 0 ft wide, the length / needs to be no more than 0 ft.you plan to use at least 50 ft of fencing. Graph the following sstem to find possible dimensions for the rectangle. # 0 + w $ 50 B Eample (page 80) Appl Your Skills. Suppose ou receive a $50 gift certificate to the Citside Music and Books store. All CDs at the store cost $9.99, and all books cost $5.99. You want to bu some books and at least one CD. a. Write a sstem of inequalities for books and CDs that describes this situation. b. Graph the sstem to show all possible solutions. c. What purchase does the ordered pair (, 6) represent? Is it a solution to our sstem? Eplain. d. Find a solution in which ou spend almost all of the gift certificate.. Business A seafood restaurant owner orders perch and salmon. He wants to bu at least 50 pounds of fish but cannot spend more than $80. Write and graph a sstem of inequalities to show the possible combinations of perch and salmon he could bu.. Earnings Suppose ou have a job in an ice cream shop that pas $6 per hour. You also have a babsitting job that pas $ per hour. You want to earn at least $60 per week but would like to work no more than hours per week. a. Graph and write a sstem of linear inequalities that describes this situation. b. Give three possible solutions to the sstem. Write a sstem of inequalities for each of the following graphs. w 0 ft Lesson 7-6 Sstems of Linear Inequalities 80-8

3 C Challenge 9. pen-ended Write a sstem of four inequalities that describes a rectangle. Graph the sstem. 0. Geometr The following sstem of inequalities > 0 describes a right isosceles triangle. > 0 a. Find m. < m + b. Find the area of the triangle. Geometr The solution region of each sstem of linear inequalities below forms a figure. (a) Describe the shape. (b) Find the vertices. (c) Find the area.. $ +. $. $ 0. $ # # 5 # $ - $ - $ - $ - + # # # a. Business A clothing store has a going-out-of-business sale. The are selling pants for $0.99 and shirts for $.99. You can spend as much as $5 and want to bu at least one pair of pants. Write and graph a sstem of inequalities that describes this situation. b. Suppose ou need to bu at least three pairs of pants. From our graph, find all the ordered pairs that are possible solutions. 6. a. Graph each inequalit.. +, - b. Writing Will the boundar lines = + and = - ever intersect? Eplain. c. Will the shaded regions ou drew in part (a) overlap? d. Does the sstem of inequalities have an solutions? 7. a. Graph the sstem of inequalities.. - 5, + b. Will the boundar lines = - 5 and = + ever intersect? Eplain. c. Describe the shape of the overlapping region. pen-ended Write a sstem of linear inequalities with the given characteristics. 8. (0, 0) is a solution. 9. Solutions are onl in Quadrant II. 0. There is no solution.. (, 7) is not a solution.. Solutions are onl in Quadrant IV.. Business A jeweler plans to produce a ring made of silver and gold. The price of gold is approimatel $0/g. The price of silver is approimatel $.5/g. She considers the following in deciding how much gold and silver to use in the ring. The total mass must be more than 0 g but less than 0 g. The ring must contain at least g of gold. The total cost of the gold and silver must be less than $60. Let s = the mass of silver in grams and d = the mass of gold in grams. a. Write and graph the four inequalities that describe this situation. b. For one solution (s, d), find the mass of the ring and the cost of the gold and silver.. Solve «$.(Hint:Write two inequalities; then graph them.) 80-8 Chapter 7 Sstems of Equations and Inequalities

4 Write a sstem of linear inequalities with the given characteristics. 5. (, 5) and (5, ) are not solutions; (5, 5) is a solution. 6. (-, ) and (, ) are not solutions; (-, 6) is a solution. 7. Sports During part of the baseball season, a plaer had 0 hits in 05 at-bats. 0 The ratio 05 gave him a.9 batting average. (Batting averages are rounded to 0 h the nearest thousandth.) The inequalit 05 a $.00 gives the number of hits h needed during his net at-bats a to reach at least a.00 average. The inequalit h # a indicates the plaer cannot have more hits than at-bats. 0 h a. Solve 05 a $.00 for h. b. Graph the sstem. c. What does a solution mean in terms of the original problem? 8. Business A drum maker sells two sizes of frame drums like the ones at the left. A -in. drum sells for $80 and an 8-in. drum sells for $0. He is tring to decide how man drums to build and considers the following: He wants to produce and sell at least $700 worth of drums. He has materials to make no more than 7 drums. He plans to make more -in. drums than 8-in. drums. He wants to make at least four 8-in. drums. a. Write and graph the four inequalities that describe this situation. b. Give one possible solution to the sstem. Standardized Test Prep Multiple Choice Short Response Etended Response Take It to the NET nline lesson quiz at Web Code: aea Which point is a solution of the following sstem?., - I. (, ) II. (, ) III. (, 9) A. I onl B. I and II C. I and III D. II onl 50. There are at most biccles and triccles in a school plaground. There are at least 7 wheels altogether. Let b equal the number of biccles and t equal the number of triccles. Which sstem describes this situation? F. b + t, G. b + t # b + t $ 7 b + t $ 7 H. b + t # I. b + t # b + t. 7 b + t # 7 5. Describe the solution to the following sstem. + $ + # 5. Suppose ou and our friends are going out for pizza. a. Write a sstem of equations for the cost of a large pizza at each restaurant, based on the information at the right. b. Solve the sstem. Interpret our results. c. Where will ou go for pizza? Eplain our reasons. Ton s Pizza Large cheese $7 Each topping $.75 Maria s Pizza Large cheese $8 Each topping $.50 Lesson 7-6 Sstems of Linear Inequalities 80-8

5 Mied Review Lesson 7-5 Graph each linear inequalit # # $ , 8 Find the slope of a line parallel to the graph of each equation = = = 0 Lesson 6-5 Lesson 5- Find the slope of a line perpendicular to the graph of each equation. 6. = 6. = = = = = 7 Write a function rule for each table. 68. f() f() f() Chapter 7 Sstems of Equations and Inequalities