# MATH 830/GRACEY EXAM 3 PRACTICE/CHAPTER 4. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 MATH 830/GRACEY EXAM 3 PRACTICE/CHAPTER Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The sum of two numbers is 3. Three times the first number equals times the second number. Find the two numbers. 1) A) 1 7 and 9 7 B) and C) 3 and 1 D) 1 and 9 ) A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and soft drinks for \$35.8. The second group bought 5 slices of pizza and soft drinks for \$7.7. How much does one slice of pizza cost? A) \$3.15 per slice of pizza B) \$1.57 per slice of pizza C) \$.07 per slice of pizza D) \$3.5 per slice of pizza ) 3) Doreen and Irena plan to leave their houses at the same time, roller blade towards each other, and meet for lunch after hours on the road. Doreen can maintain a speed of 3. miles per hour, which is 0% of Irena's speed. If the meet eactl as planned, what is the distance between their houses? A) 1 miles B). miles C) 8.9 miles D). miles 3) 1

2 ) A compan's cost for producing magazines is given b the equation = The revenue for selling magazines is given b the equation = 3. The break-even point is the point at which the cost and revenue are the same. The graphs of the two equations are shown. Use the graph to solve the sstem. = = 3 Interpret the coordinates of the solution in practical terms. ) Cost Dollars Revenue Magazines Produced and Sold A) {(750, 50)}; If 50 magazines are produced and sold, the compan will break even: both cost and revenue will be equal to \$750. B) {(50, 150)}; If 50 magazines are produced and sold, the compan will break even: both cost and revenue will be equal to \$150. C) {(750, 00)}; If 750 magazines are produced and sold, the compan will break even: both cost and revenue will be equal to \$00. D) {(750, 50)}; If 750 magazines are produced and sold, the compan will break even: both cost and revenue will be equal to \$50. 5) One number is four more than a second number. Two times the first number is more than four times the second number. A) and B) - 5 and - 9 C) 7 and 3 D) 8 and 5) ) An electronics compan kept comparative statistics on two products, A and B. For the ears 1980 to 1988, the total number of Product A ever sold (in thousands) is given b the equation = , where is the number of ears since For that same period, the total number of Product B ever sold (in thousands) is given b the equation = , where is the number of ears since Use the substitution method to solve the sstem and choose the statement that most accuratel describes the solution. A) When 388,000 of Product A had been sold, Product B had sold 1. times as man. B) At about 1. ears (to the nearest tenth) from 1980, both products had sold the same amount. C) At some point between 1980 and 1988, both products had sold 100 each. D) Product B sold 1. times as man as Product A. ) 7) A retired couple has \$10,000 to invest to obtain annual income. The want some of it invested in safe Certificates of Deposit ielding %. The rest the want to invest in AA bonds ielding 11% per ear. How much should the invest in each to realize eactl \$15,100 per ear? A) \$110,000 at 11% and \$50,000 at % B) \$110,000 at % and \$50,000 at 11% C) \$100,000 at % and \$0,000 at 11% D) \$10,000 at 11% and \$0,000 at % 7)

3 8) Devon purchased tickets to an air show for 9 adults and children. The total cost was \$50. The cost of a child's ticket was \$7 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket. A) adult's ticket: \$; child's ticket: \$17 B) adult's ticket: \$; child's ticket: \$19 C) adult's ticket: \$5; child's ticket: \$18 D) adult's ticket: \$3; child's ticket: \$1 8) 9) A vendor sells hot dogs and bags of potato chips. A customer bus 3 hot dogs and bags of potato chips for \$9.00. Another customer bus 5 hot dogs and bags of potato chips for \$ Find the cost of each item. A) \$.00 for a hot dog; \$0.75 for a bag of potato chips B) \$.00 for a hot dog; \$1.00 for a bag of potato chips C) \$.5 for a hot dog; \$1.00 for a bag of potato chips D) \$0.75 for a hot dog; \$.00 for a bag of potato chips 9) 10) One number is less than a second number. Twice the second number is 1 less than times the first. Find the two numbers. A) 1 and 1 B) 11 and 15 C) 10 and 1 D) -15 and ) 11) Jimm is a partner in an Internet-based coffee supplier.the compan offers gourmet coffee beans for \$11 per pound and regular coffee beans for \$7 per pound. Jimm is creating a medium-price product that will sell for \$9 per pound.the first thing to go into the miing bin was 1 pounds of the gourmet beans. How man pounds of the less epensive regular beans should be added? A) 17 pounds B) 1 pounds C) 18 pounds D) 15 pounds 11) 1) On a buing trip in Los Angeles, Rosaria Perez ordered 10 pieces of jewelr: a number of bracelets at \$ each and a number of necklaces at \$1 each. She wrote a check for \$180 to pa for the order. How man bracelets and how man necklaces did Rosaria purchase? A) 30 bracelets and 90 necklaces B) 5 bracelets and 95 necklaces C) 15 bracelets and 105 necklaces D) 0 bracelets and 100 necklaces 1) 13) The three angles in a triangle alwas add up to 180. If one angle in a triangle is 8 and the second is times the third, what are the three angles? A) 8, 88, B) 8, 89, 3 C) 8, 8, D) 8, 87, 5 13) 1) Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is feet more than times the width. He needs 7 feet of fencing to do the job. Find the length and width of the garden. 1) A) length: feet; width: feet B) length: 30 feet; width: 7 feet C) length: feet; width: 1 5 feet D) length: 3 feet; width: 8 feet 15) Julie and Eric row their boat (at a constant speed) 7 miles downstream for 3 hours, helped b the current. Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the current. A).5 mph B) mph C) mph D) 3 mph 15) 3

4 1) Megan is having her ard landscaped. She obtained an estimate from two landscaping companies. Compan A gave an estimate of \$0 for materials and equipment rental plus \$50 per hour for labor. Compan B gave an estimate of \$80 for materials and equipment rental plus \$0 per hour for labor. We can represent this situation with the sstem of linear equations c = Compan A c = Compan B where c is the total cost and is the number of hours of labor. Graph the sstem. What is the -coordinate of the intersection point of the graphs? Describe what this -coordinate means in practical terms. 1) c Total Cost (dollars) Hours of Labor A) 5; there is a number of hours of labor, for which both companies charge \$500. B) 5; for 5 hours of labor, both companies charge the same. C) ; for hours of labor, both companies charge the same. D) 9; for 9 hours of labor, both companies charge the same. 17) Jamil alwas throws loose change into a pencil holder on his desk and takes it out ever two weeks. This time it is all nickels and dimes. There are 8 times as man dimes as nickels, and the value of the dimes is \$5.5 more than the value of the nickels. How man nickels and dimes does Jamil have? A) 7 nickels and 5 dimes B) 5 nickels and 7 dimes C) 8 nickels and dimes D) nickels and 8 dimes 17) 18) A college student earned \$5000 during summer vacation working as a waiter in a popular restaurant. The student invested part of the mone at 9% and the rest at 7%. If the student received a total of \$39 in interest at the end of the ear, how much was invested at 9%? A) \$71 B) \$900 C) \$500 D) \$100 18) 19) A twin-engined aircraft can fl 180 miles from cit A to cit B in 5 hours with the wind and make the return trip in 8 hours against the wind. What is the speed of the wind? A) mph B) 3 mph C) 8 mph D) 80 mph 19) Decide whether or not the ordered pair is a solution of the sstem. 0) (-, 5) + = 9 - = -1 A) Yes B) No 0)

5 1) (-, ) 3 + = = - A) No B) Yes 1) Solve the sstem b the best method. ) + = 3 + = 8 A) {(, )} B) {(1, 1)} C) {(, )} D) no solution; ) 3) = = 10 A) {(-3, )} B) {(-3, 3)} D) {(-, 3)} 3) ) + = = - A) {(-, 8)} B) {(, -8)} C) {(-, -8)} D) {(, 8)} ) 5) + 8 = 0-8 = 8 A) {(, 3)} B) {(-3, )} C) {(, -3)} D) {(8, -1)} 5) Solve the sstem b the addition method. If there is no solution or an infinite number of solutions, so state. ) + 3 = - = - - A) infinite number of solutions; {(, ) + 3 = -} or {(, ) = - - } B) {(0,0)} D) {(, 3)} ) 7) 3-1 = -7 7) = - 19 A) {(-, )} B) no solution; C) {(, 1)} D) {(-1, 1)} 8) 9-9 = = - A) {(9, )} B) {(3, )} D) 1, - 1 8) 9) + = + = -5 A) {(0, 0)} B) {(0, -3)} D) {(, -5)} 9) 30) + = -1 + = -5 A) {(-5, -)} B) {(, -5)} D) {(-, -7)} 30) 5

6 31) + = = 35 A) {(1, )} B) {(0, 7)} C) {(-7, 0)} D) no solution; 31) 3) + 5 = = + A) {(-3, 0)} B) infinite number of solutions; (, ) + 5 D) {(0, -3)} = or (, ) 3 = + 3) 33) + = = 80 A) no solution; B) infinite number of solutions; {(, ) + = 0} or {(, ) 1 + = 80} C) {(5, 0)} D) {(0, 0)} 33) 3) = = -3 A) no solution; B) {(8, )} C) {(9, )} D) {(9, 1)} 3) 35) + = - - = 8 A) no solution; B) {(, -)} C) {(1, -5)} D) {(-, -5)} 35) 3) 3 - = - 5 = A) 7, - 7 B) no solution; C) infinite number of solutions; {(, ) 3 - = } or {(, ) - 5 = } 3) D) - 7, 7 37) + 30 = = 5 A) {(9, -9)} B) {(-9, 9)} C) {(-, 9)} D) {(1, -1)} 37) Solve the sstem b the substitution method. If there is no solution or an infinite number of solutions, so state. 38) = ) = A) infinite number of solutions; {(, ) = } or {(, ) = } B) no solution; C) {(-8.1, 7.75)} D) {(8.1, 7.75)}

7 39) + = = 7 A) {(5, -)} B) infinite number of solutions; {(, ) + = 18} or {(, ) 1 + = 7} D) {(0, 18)} 39) 0) = + 3 = 9 + A) 19 5, 1 5 B) no solution; C) infinite number of solutions; {(, ) = + 3} or {(, ) = 9 + } D) 1 5, ) 1) - 5 = = 1 A) {(-, 0)} B) no solution; C) {(, -1)} D) {(-5, -)} 1) ) = - + = A) infinite number of solutions; {(, ) + = } or {(, ) = -} B) {(1, 5)} D) {(1, 1)} ) 3) + = = - A) {(, 8)} B) {(-, 8)} C) {(, -8)} D) {(-, -8)} 3) ) + = - - = 11 A), 7 B) 7, - 15 C), - 15 D) 7, 15 ) 5) - 5 = + = A) infinite number of solutions; {(, ) - 5 = } or {(, ) + = } B) {(5, )} D) {(, 5)} 5) ) + = = -33 A) {(, -1)} B) {(3, 0)} D) {(-, 0)} ) 7

8 Solve the sstem b graphing. 7) 1 - = 1 7) = A) {(, 0)} B), 1 C) {(, 1)} D) {(0, )} 8) + = 7 - = ) A) {(3, -)} B) no solution; C) {(3, )} D) {(, 3)} 9) + = = - 9) A) {(-3, -)} B) {(-, )} C) {(-, -5)} D) {(, )} 8

9 50) = 5 = -3 50) A) no solution; B) infinite number of solutions; {(, ) = 5} or {(, ) = -3} C) {(5, -3)} D) {(-3, 5)} 51) + 3 = 51) = A) no solution; B) {(5, )} C) {(-5, -)} D) {(5, -)} 5) 5 + = = -5 5) A) {(-5, -)} B) {(5, 5)} C) {(-3, -5)} D) {(-5, 5)} 9

10 Solve the sstem b graphing. If there is no solution or an infinite number of solutions, so state. 53) = 0 = -5 53) A) infinite number of solutions; {(, ) = -5} or {(, ) = 0} B) no solution; C) {(0, -5)} D) {(-5, 0)} 5) - 3 = = ) A) infinite number of solutions; {(, ) - 3 = } or {(, ) = 18 + } B) {(1, 1)} D) {(-1.5, -1)} 10

11 55) + = + = 55) A) 1, 0 B) 3, 0 D) infinite number of solutions; {(, ) + = } or {(, ) + = } 5) = - + = 5) A) no solution; B) infinite number of solutions; {(, ) + = } or {(, ) = -} C) {(1, 5)} D) {(1, 1)} 11

12 Answer Ke Testname: M830E3PRAC_SCRAMBLED 1) A ) D 3) B ) D 5) C ) B 7) A 8) A 9) A 10) B 11) B 1) D 13) A 1) B 15) D 1) C 17) A 18) D 19) C 0) B 1) B ) D 3) A ) A 5) C ) A 7) A 8) C 9) C 30) A 31) B 3) D 33) B 3) D 35) B 3) A 37) A 38) D 39) B 0) D 1) A ) C 3) B ) B 5) C ) A 7) A 8) C 9) B 50) C 1

13 Answer Ke Testname: M830E3PRAC_SCRAMBLED 51) D 5) D 53) B 5) A 55) C 5) A 13

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