Chapter 1 Review Solve these equations. Solve the linear inequalities and graph the solutions on a real number line. 1. 5(x 1) + 3 = 4x 7 12.

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1 09A_MacArthur_Ch._Review.qxd //0 : PM Page Chapter Review. Solve these equations.. (x ) + = 4x 7 +. x 6 = x 9 x 4 + = + 4 x 4 + = x x + = 0 + x = x + 6 x + x = = x x 9. Twenty more than five times a number is the same as seven times that same number. What is the number? 0. A car sells for $,48.60 and this price includes 7.% sales tax. How much is the sales tax?. Find three consecutive even numbers whose sum is 7.. Solve the linear inequalities and graph the solutions on a real number line x 4 x + x + 4 x < x ( w + 4) < + w ( 8x ) + < ( 8x 6) 8. Malik scored 69, 78, 8 and 7 (out of a possible 00 points) on the four midterm exams for a math class. If the three highest scoring exams each count as 0% of the total grade, the lowest exam counts as only 0% of the total grade, and the final exam counts as 0% of the total grade, what must Malik score on the final exam to get at least 7% as the overall grade in the class? 9. Jaleigh invests a total of $0,000 in two different accounts. The riskier investment yields an annual average of % profit and the safer investment typically yields 6% profit annually. How much money should be invested in the safer account if Jaleigh needs at least $0 profit per year?

2 09A_MacArthur_Ch._Review.qxd //0 : PM Page Chapter Review. Find the slope of the line through the two given points. 0. (, ) and (, ). (4, ) and (, ). (, 9) and (, 0) Write the equation of the line, in slope-intercept form, given two pieces of information about the line.. m =, goes through the point (, ) 4. goes through the points (, 7) and (, ) x 4y = x y = + y = 9 6x y = 8 x + 4y = x y = 0 y = x + 6y = x + y = 4 9x y = 4. goes through the point (4, 0) and is parallel to the line + 4y = 6. goes through the point (, 6) and is perpendicular to the line x y = 9 7. goes through the point (0, 8) and has undefined slope 8. The plumber, Paul, charged Ann a flat fee of $0 just to come to her house. Then, his hourly labor rate was $4, prorated for parts of hours. If he was there for 4 minutes, how much was her plumbing bill?.4 Solve these systems of equations y = 7 x y = x + y = y = 6 4x y = x + y = 9 7. x + y + z = y + z = 4y + z = 8. x + y + z = y + z = 4y + z = 6 9. At Leslie s Party Store, you can purchase fancy party hats for $.0 each and party favors for $0.80 each. Carmen spent $04.0 for a total of 00 items, including only the party hats and party favors. How many party hats and how many party favors did Carmen purchase?. 40. Find the market equilibrium point given a demand equation of p + q = 49 and a supply equation of p q = Van s Furniture Store sells a popular rocking chair. They ve discovered, through market analysis, that the demand equation is p + q = 740 for this chair, and their supply equation is p = q 0. Given this information, what price should they charge for a rocking chair? How many chairs will they sell at this price?

3 09A_MacArthur_Ch._Review.qxd //0 : PM Page Chapter Review 4. Mohomodou is thinking of starting a business selling t-shirts with inspirational quotes on them. His target consumer group is comprised of wealthy clients, including celebrities. After some market research, he finds the consumers will buy 80 t-shirts if the price is $4 and will buy 00 t-shirts for a price of $6. He s willing to supply t-shirts according to the equation p + 04 = q. a. How many t-shirts will he sell if he prices each t-shirt at $? b. What price must he charge to sell 0 shirts? c. What is the market equilibrium point? 4. The demand for Ki s chocolate truffles, during the winter holiday season, is 400 when the cost is $.0 each, but demand goes up to 800 when the cost is only $ each. Assuming the demand equation is linear, find the demand equation. At what price would consumers be willing to buy 000 of Ki s truffles? 44. Given a cost equation of C = 8x and a revenue equation of R = 4x, where x is the quantity of books made and sold, how many books should be sold to break even? What is the cost of creating that many books? What is the revenue from selling those books? workshop. How many students must sign up for the workshop for Alkira to break even? She wants to keep the workshop enrollment to a maximum of 0 students. If it has a maximum capacity, what is Alkira s profit for the workshop? 47. For a cost equation given by C = + 0 and a revenue equation of R = 6.x, answer the following questions..6 a. What is the profit equation? b. What is the equilibrium point? Graph the solution set of each of these systems of inequalities x 0, y 0 + y 0 x y y x 4y 0 7x + 7y 6 x x 6 y x + x + 4y 0 4. In her retirement, my mother decided to sell her homemade jellies. Her fixed costs are $0 per month and it costs an additional $., on average, to produce one jar of jelly. She can sell each jar for $4.0. How many jars of jelly must she sell to break even? What will her profit be if she sells 0 jars this month? What will her profit be if she sells 00 jars of jelly?.. y x 4 y 4x + 8 x y + y 7 y y y x Alkira realized there is a great need for helping students overcome their fear of mathematics. She s decided to go into business offering workshops to help students overcome this fear and fulfill this need. Her fixed costs will be $40, according to her calculations, and materials will cost $40 per attendee. She s planning on charging $9 per student for participating in her. A Bikram yoga studio charges $0 per class for adults and only $6 per class for students. The studio can hold a maximum of 6 students for a class. The owner wants to bring in revenue of at least $90 for a special New Year s Eve class. Graph the possible solution set, providing also the system of inequalities for that solution set.

4 09A_MacArthur_Ch._Review.qxd //0 : PM Page 4 4 Chapter Review.7 Find both the maximum and minimum of the objective function, f, given the inequality constraints on x and y. 4. f = + y y 8 6y x 8 y x + 6. f = + y x 0, y 0 7x + y 9y 4x f = x y y 8x + 4 4x y y 8x + 40 y 4x (Refer to problem.) If the yoga studio owner has a profit equation of P = x + y, where x is the number of adult participants and y is the number of student participants, what is the maximum profit for the special New Year s Eve class? How many adult and student participants create that maximum profit?

5 09A_MacArthur_Ch._Review.qxd //0 : PM Page Chapter Review CHAPTER REVIEW ANSWER KEY. x =. x = 6. x = 4. x = 0. x = 6. x = 7. x = 8. N.S $7.60., 4 and 6. x. x x y = x x = 0 8. $.7 9. (, ) 0. (, 0). (, 9). N.S.. same line; infinitely many solutions 4. N.S.., 6. same line; infinitely many solutions 7. (,, 0) 8. (, 7, ) 9. hats, 6 party favors 40. (0, $) 4. $90; 60 chairs 4. (a) 0 shirts; (b) $; (c) (0, $8) 4. p = q + 7 ; ~$0.7 each books; $8,000; $8, jars; $7.0; $ students; $,0 47. (a) P =.x 0; (b) (88.6, $7.70) 48.. x < 4 6. w > x < at most $, undefined slope. y = + 4. y = +. y = x +

6 09A_MacArthur_Ch._Review.qxd //0 : PM Page 6 6 Chapter Review.. maximum of 9 at (, 0) minimum of 0 at (0, 0). 6. maximum of at (, 0) minimum of at (, 0). x 0, y 0 x + y 6 0x + 6y 90 9 (0, ) 7. $; 6 adults and 0 students (0,6) (9,0) (6,0) 4. maximum of 40 at (0, 8) minimum of at (, )