Solve the following base 12 and base 60 problems a. A store owner buys small, no

Question

Solve the following base 12 and base 60 problems a. A store owner buys small, novelty party favors in bags of 1 dozen and boxes of 1-dozen bags (for a total of 144 favors in a box), The store owner has 5 boxes, 4 bags, and 3 individual party favors at the start of the month. At the end of the month, the store owner has 2 boxes, 9 bags, and 7 individual party favors left. How many favors did the store owner sell? Give the answer in terms of boxes, bags and individual favors. Solve this problem by regrouping among the boxes, bags and individual party favors. b. Ruth runs around a lake two times. The first time takes 1 hour, 43 minutes and 38 seconds. The second time takes 1 hour, 48 minutes, and 29 seconds. What is Ruth’s total time for the two laps? Give the answer in hours, minutes, and seconds. Solve the following base 12 and base 60 problems a. A store owner buys small, novelty party favors in bags of 1 dozen and boxes of 1-dozen bags (for a total of 144 favors in a box), The store owner has 5 boxes, 4 bags, and 3 individual party favors at the start of the month. At the end of the month, the store owner has 2 boxes, 9 bags, and 7 individual party favors left. How many favors did the store owner sell? Give the answer in terms of boxes, bags and individual favors. Solve this problem by regrouping among the boxes, bags and individual party favors. b. Ruth runs around a lake two times. The first time takes 1 hour, 43 minutes and 38 seconds. The second time takes 1 hour, 48 minutes, and 29 seconds. What is Ruth’s total time for the two laps? Give the answer in hours, minutes, and seconds. Solve the following base 12 and base 60 problems a. A store owner buys small, novelty party favors in bags of 1 dozen and boxes of 1-dozen bags (for a total of 144 favors in a box), The store owner has 5 boxes, 4 bags, and 3 individual party favors at the start of the month. At the end of the month, the store owner has 2 boxes, 9 bags, and 7 individual party favors left. How many favors did the store owner sell? Give the answer in terms of boxes, bags and individual favors. Solve this problem by regrouping among the boxes, bags and individual party favors. b. Ruth runs around a lake two times. The first time takes 1 hour, 43 minutes and 38 seconds. The second time takes 1 hour, 48 minutes, and 29 seconds. What is Ruth’s total time for the two laps? Give the answer in hours, minutes, and seconds.

Explanation / Answer

a)

1 box = 12^2 = 144

1 bag = 12

Initial inventory = 5 boxes, 4 bags and 3 individual party favors = 5 * 12^2 + 4 * 12 + 3 * 12^0 = 771

Final inventory = 2 boxes, 9 bags and 7 individual party favors = 2 * 12^2 + 9 * 12 + 7 * 12^0 = 403

Number of favors sell = 771 - 403 = 368

368 = 2 * 12^2 + 6 * 12 + 8 * 12^0

Hence the answer will be 2 boxes, 6 bags and 8 individual favors

b) Time for first trip = 1 hour 43 minutes 38 seconds

1 hour = 3600 s, 1 minute = 60 seconds

Time for first trip = 1 hour * 3600s/1 hour + 43 min * 60s/1min + 38 s = 6218s

Time for second trip = 1 hour * 3600s/1 hour + 48 min * 60s/1min + 29s = 6509s

Total time for two laps = 6218 + 6509 = 12737s

Now converting 12737 in base 60

12737 = 3 * 60^2 + 32 * 60 + 17 * 60^0 = 3 hours 32 minutes 17 seconds

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