Math 12 EXAM #2 Name: Complete all problems in your blue book. Copy the problem into the bluebook then show all of the required work for that problem. Work problems out down the page, not across. Make only one column of work per page. Skip a line between each problem. Any work or answers completed on this test form, other than the problems that require you to graph, will not be graded. For problems that REQUIRE YOU TO GRAPH use the graphs provided on this test form and complete the work for those problems in the space next to the graph. If you feel that you need more room, then indicate next to the graph that the work is in your bluebook. Complete, organized, and correct work, using the methods taught in class and including correct use of symbols, is required to receive full credit. Partial or no credit will be given when work is missing. Each problem is worth points. SHOW ALL WORK. DO NOT ROUND ANSWERS UNLESS INSTRUCTED TO DO SO. Express answers in lowest terms. Simplify all radicals. Solve the equation. 1) 9 y - (y + 1 2 ) = 1 72 ( y - ) 72 9 y - (y + 1 2 ) = 1 72 ( y - )72 40y - 72(y + 1 2 ) = y - 40y - 72y - 6 = y - -2y - 6 = y - -6 = y - - = y -1 = y 2) (8x + 2) = (10x - ) 12 12(8x + 2) = (10x - ) 96x + 24 = 0x - 1 46x + 24 = -1 46x = -9 x = - 9 46 ) 7(x + 8) -16x = -9(x + ) + 16 7x + 6-16x = -9x - 4 + 16 6-9x = -9x - 29 6 = -29 1 4) (9x + 4) - 21x = (2x + 6) - 2 27x + 12-21x = 6x + 18-2 6x + 12 = 6x -
) 0.04(0) + 0.4x = 0.2(0 + x) 2 +.4x = 10 +.2x 2 +.2x = 10.2x = 8 x = 40 6) 1 4 17 = 1 x 1 4 x = 1(17) 4 1 4 x = 1(17)(4) x = 102 Set-up an equation and use it to solve the problem. 7) The difference between two positive integers is 2. One integer is three times as great as the other. Find the integers. x - y = 2 x = y y - y = 2 x = (16) 2y = 2 x = 48 y = 16 The integers are 16 and 48 8) If is added to a number and the sum is tripled, the result is 27 more than the number. Find the number. (x + ) = x + 27 x + 1 = x + 27 2x + 1 = 27 2x = 12 x = 6 9) Jessica has a rope that is 22 feet long. She cuts the rope into three pieces so that the largest piece is seven less than twice the middle piece and the middle piece is three more than the smallest piece. How big is the middle piece? s + (s + ) + (2m - 7) = 22 s: small piece m: middle piece = s + s + (s + ) + [2(s + ) - 7] = 22 2s + + [2s + 6-7] = 22 4s + 2 = 22 4s = 20 s = m = + m = 8 middle piece is 8 feet long 2
10) On August 1, the Davidson family received 2 pieces of mail, consisting of magazines, bills, letters, and ads. If they received the same number of magazines as letters, three more bills than letters, and five more ads than bills, how many magazines did they receive? M + B + L + A = 2 M + (M + ) + M + (B + ) = 2 M + (M + ) + M + (M + + ) = 2 4M + 11 = 2 4M = 12 M = magazines M: # of magazines B = # of bills L: # of letters = M A: # of ads 11) If three times the smaller of two consecutive integers is added to four times the larger, the result is 46. Find the smaller integer. 4 x + 1 + x = 46 4x + 4 + x = 46 7x + 4 = 46 7x = 42 x = 6 12) Find the measure of an angle such that the difference between its supplement and times its complement is 48. 180 - x - 90 - x = 48 18 - x - 270 + x = 48 2x - 90 = 48 2x = 18 x = 69 1) A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 20. Find the length of a side. 4x = 9x - 20 -x = -20 x = 4 14) The sum of three consecutive odd integers is 249. Find the integers. x + x + 2 + x + 4 = 249 x + 6 = 249 x = 24 x = 81 81 + 2 = 8 81 + 4 = 8
1) A pharmacist found at the end of the day she had as many prescriptions for antibiotics as tranquilizers. She had 64 prescriptions altogether. How many did she have for antibiotics? A = T A + T = 64 A: # of antibiotics T: # of tranquilizers T + T = 64 A = (24) T + T = 64() A = 40 t + T = 192 8t = 192 T = 24 16) A merchant has coffee worth $0 a pound that she wishes to mix with 80 pounds of coffee worth $80 a pound to get a mixture that can be sold for $70 a pound. How many pounds of the $0 coffee should be used? 0x + 80(80) = 70(x + 80) 0x + 6400 = 70x + 600 6400 = 40x + 600 800 = 40x 20 = x 17) A chemist has two solutions of HCL. One has a 40% concentration and the other has a 2% concentration. How many liters of each must be mixed to obtain 98 liters of a 4% solution?.40x +.2y =.4(98) x + y = 98.40(98 - y) +.2y =.2 x = 98 - y 9.2 -.40y +.2y =.2 x = 98-9.2 -.1y = -.88 x = 8.8 y = 9.2 18) A woman has $1.70 in dimes and nickels. She has 2 more dimes than nickels. How many nickels does she have?.10d +.0n = 1.70 d: # of dimes = n + 2.10(n + 2) +.0n = 1.70 n: # of nickels.10n +.20 +.0n = 1.70.1n +.20 = 1.70.1n = 1.0 n = 100 19) Roberto invested some money at 7%, and then invested $000 more than twice this amount at 12%. His total annual income from the two investments was $4940. How much was invested at 12%?.07x +.12(2x + 000) = 4940 2(14000) + 000.07x +.24x + 600 = 4940 28000 + 000.1x + 600 = 4940 $,000 @ 12%.1x = 440 x = 14000 4
20) A truck enters a highway driving 60mph. A car enters the same highway at the same place 10 minutes later and drives 72mph in the same direcrtion. How long will it take the car to pass the truck? 60 t + 10 60 = 72t 60t + 10 = 72t 10 = 12t 10 12 = t 6 = t 21) Two sides of a triangle have the same length. the third side measures 6m less than twice the common length. The perimeter of the triangle is 10m. What are the lengths of the three sides? x + x + (2x - 6) = 10 2(4) - 6 4x - 6 = 10 8-6 4x = 16 2 x = 4 the sides measure 4m, 4m, 2m Use a proportion to solve the problem. 22) On a map of the Thunderbird Country Club golf course, 2. inches equals 60 yards. How long is the 6th hole if the map shows 16 inches? 2.in 60yd = 16in x 2.x = 60(16) x = 960 2. x = 84yd Find the measure of each marked angle. 2) (11x + 2) (14x + ) (11x + 2) + 14x + = 180 11(7) + 2 180-79 2x + = 180 77 + 2 101 2x = 17 79 x = 7
Solve the formula for the specified variable. 24) F = 9 C + 2 for C F - 2 = 9 C 9 F - 2 = 9 C 9 9 F - 2 = C Find the unit price for each item to the nearest cent. Tell which brand is the better buy. 2) Brand A 2 oz for $8.64 Brand B 28 oz for $7.00 Brand A $8.64 2oz Brand B $7.00 28oz $.27/oz $.2/oz Brand B is the better buy CHOOSE ONLY ONE BONUS QUESTION TO DO. (10 points) Solve the problem. 26) A reservation clerk worked 9 hours one day. She spent twice as much time entering new reservations as she did verifying old ones and one and a half as much time calling to confirm reservations as verifying old ones. How much time did she spend entering new reservations? 27) It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 0 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength? 6