\fMath 009 Midterm Exam Page 2 Did you read the rules for showing work on page 1 of the midterm exam? If not, please go back to page 1 now and read them. If you do not show work correctly, you will not earn full credit. 1) Simplify the expression. 4 3(6 ) 12(9) 2) Simplify the expression. Show all work and write the answer in lowest terms. 1 2 4 3 2 ( )( ) ( ) 2 3 3) Solve for x. Show all work and show the complete check of your answer. 14( 5 x 6 )=6 ( x +1 )5 Math 009 Midterm Exam 4) Solve for x. Round your answer to nearest hundredth. Show all work and show the complete check of your answer. 1.5 ( 4x )=1.3(2x) 5) Solve for x. Show all work and show the complete check of your answer. 2 1 3 4 x = x 5 4 10 5 6) Solve for x. Show all work and show the complete check of your answer. x4 x2 5 = 2 3 6 Page 3 Math 009 Midterm Exam Page 4 To earn full credit for questions 8 to 15, show your work for each of the following steps:: Set up a variable dictionary. Set up an equation. Solve the equation. Answer the question. Look back. 7) Courtney recently inherited $25,000. She invests the amount in two different accounts, a money market account paying 8% interest, and a certificate of deposit paying 9% interest. She earns a total of $2135 interest from both accounts in one year. How much did she invest in each account? Math 009 Midterm Exam Page 5 8) The three sides of a triangle are consecutive odd integers. If the perimeter of the triangle is 87 feet, find the lengths of the sides of the triangle. 9) A youth organization collected nickels and dimes for a charity drive. By the end of the 1-day drive, the youth had collected $56.35. If there were three times as many dimes as nickels, how many of each type of coin was collected? Math 009 Midterm Exam Page 6 10) The area of a triangle is 20 square feet and the base is 4.5 feet. Use the formula for the area of a triangle to find the height of the triangle. Round your answer to the nearest tenth. 11) Jordan runs a business making mailboxes. Each month she has fixed costs of $155. For each mailbox she makes, she incurs an additional cost of $5.75. If her total costs for the month were $402.25, how many mailboxes did she build? Math 009 Midterm Exam Page 7 12) There are 110 calories per 28.4 grams of a cereal. Set up and solve a proportion to find how many calories are in 42.6 grams of this cereal. 13) A climber is resting at a height of 21 feet while on the Ultimate Climbing Tower. If this is 65% of the tower's total height, find the height of the tower. Set up a percent equation to solve this problem. Round your answer to the nearest tenth. Math 009 Midterm Exam Page 8 14) A furniture company currently produces 6250 chairs per month. If production decreases by 8.2%, use the formula for percent decrease to find the new number of chairs produced each month. Round your answer to the nearest whole number. 15) Tanya borrows money at 3.25% simple interest per year from a local bank. At the end of 4 months, she owes $260 in interest. Use the simple interest formula to find the principal amount borrowed. End of midterm exam: please do not forget to write and sign (or type) the required statement explained in the box on page 1 of the midterm exam. \fMath 009 Midterm Exam Page 2 Did you read the rules for showing work on page 1 of the midterm exam? If not, please go back to page 1 now and read them. If you do not show work correctly, you will not earn full credit. 1) Simplify the expression. 4 3(6 ) 12(9) 4 3+ 6 12+9 1.7 3 1.7 10 3 10 17 30 Math 009 Midterm Exam 2) Simplify the expression. Show all work and write the answer in lowest terms. 1 2 4 3 2 ( )( ) ( ) 2 3 ( 212 )( 49 ) ( 16 )( 49 ) (1 3 )(4 2) 18 11 18 3) Solve for x. Show all work and show the complete check of your answer. 14( 5 x 6 )=6 ( x +1 )5 145 x +6=6 x65 14 +6 5 x = 6 x56 20 5 x = 6 x11 20 +11 = 6 x +5 x 31 = x x=31 14((5 31)6 )=6 (31+1 ) 5 14(1556 ) =6 (30 ) 5 14+155+ 6=1805 175 = 175 Page 3 Math 009 Midterm Exam 4) Solve for x. Round your answer to nearest hundredth. Show all work and show the complete check of your answer. 1.5 ( 4x )=1.3(2x) 61.5 x=2.61.3 x 62.6=1.3 x+1.5 x 3.4=0.2 x 0.2 x 0.2=3.4 0.2 x=17 1.5 ( 417 ) =1.3(217) 1 .5 13 =1.3 15 19.5=19.5 19. 5 =19.5 Page 4 Math 009 Midterm Exam 5) Page 5 Solve for x. Show all work and show the complete check of your answer. 2 1 3 4 x = x 5 4 10 5 2 3 1 4 x x= 5 10 4 5 ( 2 x 2 )(3 x 1) ( 1 5 ) (4 4) = 10 20 4 x3 x 516 = 10 20 x 11 = 10 20 x 11 10 10 = 20 x= 10 11 2 ( 25 112 ) 14 =( 103 112 ) 11 1 5 4 = 33 20 4 5 4 5 (11 4 ) (1 5) 20 = (33 1)( 4 4) 20 49 20 = 49 20 -20 49=49 -20 Math 009 Midterm Exam 6) Page 6 Solve for x. Show all work and show the complete check of your answer. x4 x2 5 = 2 3 6 x 4 x 2 2 2 3 3 x x 2 3 5 2 6 4 = 6+3 + 2 ( x 3 ) ( x 2) 6 x 6 5 = 6 = 21 6 x 6 = 21 6 = ( 5 1 )+ (2 2 ) +(4 3) 6 6 x=21 214 212 5 = 2 3 6 17 23 5 = 2 3 6 ( 17 3 )(23 2) 5 = 6 6 5 5 = 6 6 To earn full credit for questions 8 to 15, show your work for each of the following steps:: Set up a variable dictionary. Math 009 Midterm Exam 7) Page 7 Set up an equation. Solve the equation. Answer the question. Look back. Courtney recently inherited $25,000. She invests the amount in two different accounts, a money market account paying 8% interest, and a certificate of deposit paying 9% interest. She earns a total of $2135 interest from both accounts in one year. How much did she invest in each account? Solution Let the amount saved in market account be P1 and rate in decimals be R1 The amount saved in a certificate of deposit be P2 and rate in decimals be R2 Let total interest be I Let amount be A. Let time in one year be T The equation A = $2,135 +$25,000 = $27,135 I= P1 R1 T + P2 R2 T I= P1 0.08 1 + P2 0.09 1 2,135= 0.08 P1 + 0.09 P2 $25,000 = P1 + P2 P1 = $25,000 - P2 2,135 = 0.08($25,000 - P2) + 0.09P2 Solution to the equation 2,135 = $2000 -0.08P2 + 0.09P2 $2,135-2000 = 0.09 P2 - 0.08P2 135 = 0.01 P2 P2= $135/0.01 P2 = $13,500 P1 = $25,000 - $13,500 P1 = 11,500 She saved $11,500 in market account and $13,500 in a certificate of deposit account $11,500 + $13,500 = $25,000 $25,000 = $25,000 Math 009 Midterm Exam 8) The three sides of a triangle are consecutive odd integers. If the perimeter of the triangle is 87 feet, find the lengths of the sides of the triangle. Let the sides of the triangle be A, A+2 and A + 4 Let feet be 'f' The equation. A + A +2f + A +4f + = 87f 3A = 87f - 2f - 4f 3A = 87f - 6f 3A = 81f Solution A = 81f 3 A = 27f The lengths are; 27f, 27f + 2f = 29f, 27f + 4f = 31f. 27f + 27f +2f + 27f +4f = 87f 87f = 87f Page 8 Math 009 Midterm Exam 9) Page 9 A youth organization collected nickels and dimes for a charity drive. By the end of the 1-day drive, the youth had collected $56.35. If there were three times as many dimes as nickels, how many of each type of coin was collected? In United states, a nickel = 5cents And a dime = 10cents Let the total number of dime collected be 'D' And total number of nickel collected be 'N' The equation. 0.1D +0.05 N = $56.35 Solving the equation D = 3N 0.1(3N) + 0.05N = $56.35 0.35N = $56.35 N = $56.35 0.35 N = 161 D = 161 3 D = 483 Dimes were 483 And nickels were 161 (0.1483) +( 0.05 161) = 56.35 $48.30 + $8.05 = $56.35 $56.35 = $56.35 10) The area of a triangle is 20 square feet and the base is 4.5 feet. Use the formula for the area of a triangle to find the height of the triangle. Round your answer to the nearest tenth. Let height be 'H', Base be 'B', area be 'A', and feet be 'f' The equation A = BH Solution of the equation 20 = 4.5f H 20f 2 = 4.5f H H = 40f 4.5f = 8.8889f The height of the triangle = 8.9feet 20f = 8.9f 4.5f 20f = 20.025f 20f = 20f Math 009 Midterm Exam 11) 12) Page 10 Jordan runs a business making mailboxes. Each month she has fixed costs of $155. For each mailbox she makes, she incurs an additional cost of $5.75. If her total costs for the month were $402.25, how many mailboxes did she build? Solution Let the total number of mailboxes be M, Additional cost per mailbox be A Fixed costs per month be F Total cost per month be T. The equation M = (T- F) A Solution to the equation. M = (402.25 - 155) 5.75 M = 247.25 5.75 M = 43 She built 43 mailboxes for the month. 43 = (402.25 - 155) 5.75 43 = 247.255.75 43 = 43 There are 110 calories per 28.4 grams of a cereal. Set up and solve a proportion to find how many calories are in 42.6 grams of this cereal. Solution. Let the number of calories in 28.4 cereals be C1, Number of calories in any other grams of cereal be C2, Let 28.4grams of cereal be G1, Let any other grams of cereals be G2 The equation C2 = (G2 C1) G1 Solution to the equation C2 = (42.6 110) 28.4 C2 = 4686 28.4 C2 = 192. 049 42.6 grams has 192 calories. 192 = (46.6 110) 28.4 192 = 4686 28.4 192 = 192 Math 009 Midterm Exam 13) Page 11 A climber is resting at a height of 21 feet while on the Ultimate Climbing Tower. If this is 65% of the tower's total height, find the height of the tower. Set up a percent equation to solve this problem. Round your answer to the nearest tenth. Let the climber's height be H1, The height of the tower be H Let feet be f The equation H = (H1 100%) 65% Solution to the equation H = (21f 100%) 65% H = 2100 65 H = 32.3077f The height of the Tower = 32.3feet 32.3f = 2100/65 32.3f = 32.3f Math 009 Midterm Exam 14) Page 12 A furniture company currently produces 6250 chairs per month. If production decreases by 8.2%, use the formula for percent decrease to find the new number of chairs produced each month. Round your answer to the nearest whole number. Let decrease be D Normal production per month be N Let number of chairs produced each month be C %Decrease be P. Equation P = (DN) 100% C=N-D Solution to the equation 8.2% = (D6250) 100% D = (8.2%100%) 6250 D = 512.5 D = 513 Number of chairs produced each month = 6250 - 513 Number of chairs produced each month = 5737 5737 = 6250 -513 5737 = 5737 Math 009 Midterm Exam Page 13 15) Tanya borrows money at 3.25% simple interest per year from a local bank. At the end of 4 months, she owes $260 in interest. Use the simple interest formula to find the principal amount borrowed. Let interest be I, Principal amount be P, Rate be R, And time of one year be T Equation I = (PRT)/100 P = (I 100%)(RT) Solution to the equation P = ($260 100%) (3.25% 4/12) 26000 1.0833 P = $24000.74 The amount borrowed = $24000.70 $24000.70 = ($260 100%) (3.25% 4/12) $24000.70 = $26000 1.0833 $24000.70 = $24000.70 End of midterm exam: please do not forget to write and sign (or type) the required statement explained in the box on page 1 of the midterm exam