1) The product of 7 x 7 may be written as 72, 6 x 6 x 6 as 63, and 5 x 5 x 5 x 5 as 54. Let A = 25, B = 34, C = 43, and D = 52. Write A, B, C, and D in order of their values beginning with the smallest
value at the left. 2) The cost of mailing a letter firstclass is $0.29 for the first ounce and $0.23 for each additional ounce. A letter weighs exactly N ounces where N is a natural number, and the total mailing cost is $1.90. What is the value of N? 3) A group of 30 bikers went on a trip. Some rode bicycles and the others rode "tandems." (A tandem is a bicycle that is ridden by 2 people at the same time). If the total number of bicycles and tandems was 23, how many tandems were used? Solutions 1) A = 2 x 2 x 2 x 2 x 2 = 32; B = 3 x 3 x 3 x 3 = 81; C = 4 x 4 x 4 = 64; D = 5 x 5 = 25. Answer: D, A, C, B; or 52, 25, 43, 34; or 25, 32, 64, 81. 2) Since the cost of the first ounce was $0.29, the total cost of the remaining ounces was $1.61. Since the cost of each of the remaining ounces was $0.23 per ounce, the number of remaining ounces was $1.61/$0.23 = 7. The total number of ounces in the letter was 8. 3) If there were no tandems on the trip, only 23 people could have gone on the trip. Then 7 people of the 30 would have been left out. There must have been 7 tandems for the 7 extra people.
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