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 Mathematical Puzzles Puzzle 17 Last weekend I was given my pocket money, which is meant to last me all week. On Monday, I spent a quarter of my money on clothes. On Tuesday, I spent one third of my remaining money on a CD. On Wednesday I spent half of my remaining money on sweets. Finally on Thursday I spent my last £1.25 on a comic. How much pocket money did I receive? [Ref: ZZJG] © Kevin Stone Direct Link: www.brainbashers.com?ZZJG Hint: It might be easier to work backwards. Answer: £5.00. Working backwards: On Thursday I had £1.25. On Wednesday I had £1.25 x (1 ÷ one half) = £2.50. On Tuesday I had £2.50 x (1 ÷ two thirds) = £3.75. On Monday I had £3.75 x (1 ÷ three quarters) = £5.00. Puzzle 18 Three teachers were discussing how long they had been teaching. Adrian and Betty had been teaching for a total of 36 years. Charles and Betty had been teaching for a total of 22 years. Charles and Adrian had been teaching for a total of 28 years. How long had each been teaching? [Ref: ZKLD] © Kevin Stone Direct Link: www.brainbashers.com?ZKLD Hint: Adrian had been teaching 6 years longer than Betty. Answer: Adrian had been teaching 21 years. Betty had been teaching 15 years. Charles had been teaching 7 years. Adrian and Betty had been teaching for a total of 36 years. Charles and Betty had been teaching for a total of 22 years. Charles and Adrian had been teaching for a total of 28 years. Let Adrian = A, Betty = B and Charles = C, then:    A + B = 36       [1]    C + B = 22       [2]    C + A = 28       [3] If we use [3] - [2] we have:    A - B = 6        [4] If we use [1] + [4] we have:    2A = 42     A = 21 By [1] B = 15. By [3] C = 7. Puzzle 19 Tommy: "How old are you, Mamma?" Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years." Tommy: "That's a lot, isn't it? And how old are you, Papa?" Papa: "Just six times as old as you, my son." Tommy: "Shall I ever be half as old as you, Papa?" Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day." Tommy: "And supposing I was born before you, Papa; and supposing Mamma had forgot all about it, and hadn't been at home when I came; and supposing..." Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache." Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of Mamma? [Ref: ZPYU] Mamma's Age. Amusements In Mathematics by Henry Ernest Dudeney (1917). Direct Link: www.brainbashers.com?ZPYU Hint: The answer involves years and months. Answer: The age of Mamma must have been 29 years 2 months. That of Papa, 35 years; and that of the child, Tommy, 5 years 10 months. Added together, these make seventy years. The father is six times the age of the son, and, after 23 years 4 months have elapsed, their united ages will amount to 140 years, and Tommy will be just half the age of his father. The answer above is taken from the original book, here is another version of the answer:If we call Tommy T, Mamma M and Papa P we can see that: "our three ages add up to exactly seventy years" leads to    T + M + P = 70 (1) "Just six times as old as you" leads to    P = 6 x T (2) In an unknown number of years (Y) "Shall I ever be half as old as you" leads to:    P + Y = 2 x (T + Y) (3) and "our three ages will add up to exactly twice as much as to-day" leads to:    (T + Y) + (M + Y) + (P + Y) = 140 which can be written as    T + M + P + 3Y = 140 (4) We can see from (4) and (1) that    3Y = 70 so    Y = 70 ÷ 3   (5) Using (2) and (5) in (3) we have                  P + Y = 2 x (T + Y)    6 x T + 70÷3 = 2 x (T + 70÷3)           4 x T = 70÷3               T = 70÷12 (6) We can now use (6) in (2) to see that:    P = 6 x T    P = 6 x 70÷12    P = 70÷2 And using the values for T and P in (1) we have:                          T + M + P = 70     70÷12 + M + 70÷2 = 70 Multiply throughout by 12 to give:    70 + 12 x M + 420 = 840               12 x M = 840 - 420 - 70               12 x M = 350                    M = 350÷12 So: Tommy = 70÷12   = 5.83333  = 5 years 10 months.     Papa  = 70÷2    = 35       = 35 years.     Mamma = 350÷12  = 29.1666  = 29 years 2 months. Puzzle 20 What number is... ...three quarters of eight ninths of one half of 2001? [Ref: ZRTD] © Kevin Stone Direct Link: www.brainbashers.com?ZRTD Hint: Can the fractions be simplified? Answer: 667.3   8   1   24   1 - x - x - = -- = - 4   9   2   72   3 And 1/3 x 2001 = 667.

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