38 CHAPTER 1 Critical Thinking Skills 48. Balancing a Scale On a balance scale, three green balls balance six blue balls, two yellow balls balance five blue balls, and six blue balls balance four white balls. How many blue balls are needed to balance four green, two yellow, and two white balls? 16 blue 49. Palindromes How many three-digit numbers greater than 100 are palindromes? 90 50. Figures Draw the next figure in the pattern. * , , , , . . . 51. Patterns How many shaded tiles will be required to build the sixth figure in the following pattern? 61 52. Sum of Numbers Place the numbers 1 through 12 in the 12 circles so that the sum of the numbers in each of the six rows is 26. Use each number from 1 through 12 exactly once. * 53. People in a Line People stand in a line at movies, the grocery store, and many other places. a) In how many ways can two people stand in a line? 2 b) In how many ways can three people stand in a line? 6 c) In how many ways can four people stand in a line? 24 d) In how many ways can five people stand in a line? 120 e) Using the results from parts (a) through (d), make a conjecture about the number of ways in which n people can stand in a line. n n n ( 1)( 2) 1, − − … (or n!), where n = the number of people in line 40. Microbes in a Jar A colony of microbes doubles in number every second. A single microbe is placed in a jar, and in an hour the jar is full. When was the jar half full? 59 min 59 sec 41. Brothers and Sisters A boy named Jim has four more brothers than sisters. How many more brothers than sisters does his sister Mary have? 6 42. A Missing Dollar Three friends check into a single room in a motel and pay $10 apiece. The room costs $25 instead of $30, so a clerk is sent to the room to give $5 back. The friends each take back $1, and the clerk is given a $2 tip. Now each of the friends paid $9, a total of $27, and the clerk received $2. What happened to the missing dollar? * 43. Average Grade An average grade of 80 on all exams in a course is needed to earn a B in the course. On her first four exams, Jacqueline’s grades are 93, 88, 81, and 86. What is the minimum grade that Jacqueline can receive on the fifth exam to earn a B in the course? 52 44. Tax and Tip The cost of the Freemans’ meal before tax and tip is $79.43 a) Determine the cost of the meal including sales tax of 7%. $84.99 b) If the Freemans wish to give their restaurant server a 25% tip on the pretax cost of the meal, determine the amount of the tip. $19.86 c) Determine the entire cost of the Freemans’ meal, including the tax and the tip. $104.85 45. Volume of a Cube Here is a flat pattern for a cube to be formed by folding. The sides of each square are 6 cm. Find the volume of the cube. 46. The Heavier Coin You have 13 coins, which all look alike. Twelve coins weigh exactly the same, but the other one is heavier. You have a pan balance. Tell how to determine the heavier coin in just three weighings. * 47. The Sum of Numbers Determine the sum of the first 500 counting numbers. (Hint: Group in pairs.) 125,250 216 cm3 *See Instructor Answer Appendix
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