數學.............20分

10.120 stamps are divided among Mary,Peter and Bettey.If Peter gets half(一半) as many stamps as Mary,and Betty gets three times as many as Peter.How many does each get?

120張郵票分給Mary, Peter和Bettey. 如果Peter分到的郵票是Mary的郵票的一半, 而Betty分到的郵票是Peter的三倍, 那麼他們三人各得多少郵票呢?

Answer:
Let P be the number of stamps Peter gets
Let M be the number of stamps Marry gets
Let B be the number of stamps Bettey gets

2P=M
B=3P

P+M+B=120
P+2P+B=120 because M=2P
P+2P+3P=120 because B = 3P
6P=120
P=20

Peter gets 20 stamps
Mary (=2P) gets 40 stamps
Bettey (=3P) gets 60 stamps


11.The sum of two consecutive even numbers is 86.Find the numbers.

兩個連續的雙數的總和是86. 兩個雙數分別是甚麼呢?

Answer:
Let the smaller even number be X
The bigger consecutive number must be X+2

X + (X+2) = 86
2X + 2 = 86
2X = 86 - 2 = 84
X = 42

Therefore, the two consecutive even numbers are 42, 44.

2007-07-21 23:43:20 補充：
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10. 把120枚郵票分給 Mary, Peter 和 Betty. 已知 Peter 所得的郵票是 Mary 所得的一半, 而 Betty 所得的郵票是 Peter 所得的三倍, 他們各自分得郵票是多少?

設 Mary, Peter 和 Betty 所分得的郵票數量分別為 M, P 和 B, 可得出以下數式 :
M + P + B = 120 --------------(a)
P = 0.5M --------------(b)
B = 3P ------------(c)

將 (b) 代入 (c) :
B = 3 x 0.5 M = 1.5M ------------(d)

將 (b) 及 (d) 代入 (a):
M + 0.5M + 1.5M = 120
=> 3M = 120
=> M = 40 ------------(e)

將 (e) 代入 (b) :
P = 0.5(40) = 20

將 (e) 代入 (d) :
B = 1.5 (40) = 60

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11. 兩個連續偶數之和是 86, 這兩個數是甚麽?

設該兩個數是 X 和 Y, 得出以不算式:
X + Y = 86 ----------(a)
Y = X + 2 ----------(b)

將 (b) 代入 (a) :
X + (X + 2) = 86
=> 2X + 2 = 86
=> 2X = 84
=> X = 42 ---------(c)

將 (c) 代入 (b) :
Y = 42 + 2 = 44