Math 60 Textbook : Elementary Algebra : Beginning Algebra, 12 th edition, by Lial Remember : Many homework exercises are used to teach you a concept we did not cover in class. It is important for you to attempt ALL homework problems assigned. Ch 2: Linear Equations and Inequalities in One Variable 2.1: 5, 27, 35, 39, 43, 47, 49, 57, 59, 67 79 odd 2.2: 5, 9, 33, 41, 45, 55, 57, 65 75 odd 2.3: 17 27 odd, 31, 33, 39, 43, 45 65 eoo, where eoo means every other odd 2.8: 19 23 odd, 27 35 odd, 39 63 eoo UPDATE for # s 19 23 odd, 27 35 odd, 39 63 eoo: The directions for these problems read, Solve each inequality. Write the solution set in interval notation, and graph it. Instructor s revised directions for # s 19 23 odd, 27 35 odd, 39 63 eoo: Solve and graph the solution set on a number line. Please note: Instructor has provided solutions to some of the problems from Section 2.8. Answer key to select Section 2.8 textbook exercises Revised directions for the problems that fall in the # s 19 63 block: Solve and graph the solution set on a number line. 19. z 1 27. x < 6 1 6 21. k 5 5 29. y 10 10 23. n < 11 11 31. t < 1 3 (answer key continues on the next page)
Answer key to select Section 2.8 textbook exercises, continued Revised directions for the problems that fall in the # s 19 63 block: Solve and graph the solution set on a number line. 33. x 0 47. x < 3 2 0 35. r > 20 20 51. x 0 3 2 0 37. x 3 3 55. x 4 4 39. x 3 3 59. p < 32 32 43. r 5 5 63. x 5 12 5 12 Solutions to the problems that fall in the # s 67 72 block: 68. x < 1 70. x 12 72. x > 60 Upcoming lecture note tip: You will need to bring a ruler or some other straight edge for Chapter 3. We may finish this Chapter sooner than you d think, so please bring it to class everyday starting tomorrow. (homework assignment for the rest of Chapter 2 continues on the next page)
Math 60 Textbook : Elementary Algebra : Beginning Algebra, 12 th edition, by Lial Remember : Many homework exercises are used to teach you a concept we did not cover in class. It is important for you to attempt ALL homework problems assigned. Ch 2: Linear Equations and Inequalities in One Variable, continued Please note: You cannot run away from word problems, so please don t ignore them as you do your homework. Your first midterm will have a handful of word problems. 1.2: 39 52 ALL do these exercises before you start Section 2.4 (answers provided below) 2.4: 5 13 odd, 17, 37, 39, 41, supplemental problems (see next page please do them) 2.5: 39, 41, 43, supplemental problems (see next page please do them) 2.6: 29 43 odd, 44, 53, 55, 57, 65 70 ALL, 89 2.7 11, 25, 27, 29, 31, 34, 37, 47 53 odd, supplemental problems (see next page) 40. 15x 42. x + 6 44. x 7 Answer key to select Section 1.2 textbook exercises 46. 4 x 48. 8 x 50. x 18 or x 18 52. 9(x + 5) Answer key to select Section 2.6 textbook exercises 66. x = 9 68. x = 3 70. x = 3, y = 5.5 Answer key to select Section 2.7 textbook exercises 34. adult tickets: 372, children s tickets: 228 Homework: Section 2.4 supplement (from XtraPractice: Applications of Integers) 1. Six more than five times a number is that number increased by 21. Find the number. 2. The sum of four consecutive odd integers is 0. Find the integers. 3. The sum of five consecutive even integers is 70. Find the integers. 4. Four times the largest of three consecutive integers is nine less than five times the smallest integer. Find the integers. 5. The sum of five consecutive integers is 70. Find the numbers. 6. The sum of three consecutive even integers is 12. Find the integers. ANSWER (1) 15/4 (2) 3, 1, 1, 3 (3) 10, 12, 14, 16, 18 K E Y (4) 17, 18, 19 (5) 12, 13, 14, 15, 16 (6) 6, 4, 2
Homework: Section 2.5 supplement (these types of problems are briefly discussed in Section 2.4, #45 and #46, page 140) 1. Find the measure of all three angles. (x + 60) x x 2. One angle of a triangle is 10 less than three times the smallest angle, and the third angle is 20 more than the smallest angle. Find the measures of the three angles. 3. One angle of a triangle is 28 more than twice the smallest angle, and the third angle is 10 less than three times the smallest angle. Find the measures of the three angles. Answer key: 1. 40, 40, 100 2. 34, 54, 92 3. 27, 71, 82
Homework: Section 2.7 supplement (Modified from Xtra Practice: Simple Interest) Example: Panchito purchased some municipal bonds yielding 7% annually and some certificates of deposit yielding 9% annually. If his investment amounts to $19,000 and the annual income is $1590, then how much money did he invest in the bonds and how much did he invest in the certificates of deposit? Solution: Let x = the amount invested at 7% P r t = I Account 1 x 0.07 1 yr 0.07x (bonds) Account 2 19,000 x 0.09 1 yr 0.09(19,000 x) (certificates) total $19,000 $1590 So, interest earned @ 7% + interest earned at 9% = total interest earned 0.07x + 0.09(19,000 x) = 1590 x = 6000 Therefore, Amountt invested @ 7% Amount invested @ 9% x 19,000 x 6,000 19,000 6,000 = 13,000 Answer: $6,000 was invested in municipal bonds, and $13,000 was invested in certificates of deposit. or just: $6,000 was invested at 7%, and $13,000 was invested at 9%. Wait! Does your answer make sense? $6,000 + $13,000 = $19,000 (Interest @ 7%) + (Interest @ 9%) = 6,000(.07)(1) + 13,000(.09)(1) = $1590 1. Panchito has $12,000 to invest. He deposits a portion of it into an account earning 2.75% and the rest at 5.2% annual simple interest. After 1 year, he has earned $535.80 in interest. How much did Panchito deposit into each account? 2. Panchito has $10,200 to invest. He invests part of it at 6% annual interest and the rest at 9.25% annual interest. If the amount of interest earned each year is $1,315.50, then how much was invested at each rate? 3. Panchito has some money invested at 6.75% and $3,000 less than that at 1.25% annual interest. If the annual income for the two investments is $842.50, then find the amount of money he has invested at each rate. 4. Panchito invests some money in government bonds earning 6.5% annual simple interest. He invests the same amount in utility stocks that earn 7% annual simple interest. He also decides to invest $15,000 less than twice what he s invested in the government bonds in an account earning 8% annual simple interest. The total annual interest earned from the investments was $5437.50. How much was invested at each rate? Answer key: 1. $3,600 at 2.75%, $8400 at 5.2% 2. $6,200 at 6%, $10,200 at 9.25% 3. $11,000 at 6.75%, $8,000 at 1.25% 4. $22,500 at 6.5%, $22,500 at 7%, $30,000 at 8% (To check your answers by hand, verify that the total interest checks out)
So, the nickels Homework: Section 2.7 supplement (Modified from Xtra Practice: Money, Money, Money... Money!!!) Sample: Panchito s piggy bank contains 18 coins in nickels and dimes. The coins have a total value of $1.30. Find the number of nickels and dimes in the bank. Solution 1: ( ) ( ) Solution 2: ( $ ) ( $ ) Q V = T Q V = T nickels n 5 5n nickels n 0.05 0.055n dimes 18 n 10 10(18 n) dimes 18 n 0.10 0.10(18 n) total 18 130 total 18 1.30 + the dimes = total value 5n + 10(18 n) = 130 n = 10 Nickels : n 10 Dimes : 18 n 18 10 = 8 So, the nickels + the dimes = total value 0.05n + 0.10(18 n) = 1.30 n = 10 Nickels : n 10 Dimes : 18 n 18 10 = 8 Remember: It doesn t matter if you work in terms of cents ( ) or dollars ($). Either way, you still get that... There are 10 nickels and 8 dimes in the piggy bank. Wait! Does your answer make sense? 10 nickels + 8 dimes = 18 coins 10 nickels + 8 dimes = 50 + 80 = 130 = $1.30 1. Panchito s piggy bank contains 6 coins in dimes and quarters. The coins have a total value of 90. Find the number of dimes and quarters in the bank. 2. Panchito s piggy bank contains 14 coins in nickels and quarters. The coins have a total value of $2.10. Find the number of nickels and quarters in the bank. 3. Panchito s piggy bank contains 20 coins in pennies and nickels. The coins have a total value of $0.40. Find the number of pennies and nickels in the bank. Note: An answer key will not be provided, but please don t panic. You can quickly check your solutions. Verify that the total number of coins checks out, and that it also amounts to the total money.