Exploring Mathematics F2A 數學

William

2009-12-06 7:43 am

Exploring Mathematics 2A EX5F(P.163) 17題
有冇人可以教我做?
Substitudetion & elimination
題目:
If the numerator and the denominator of a fraction are both decreased by 1, the resulting fraction is 1/2. 2/3 will be obtaines if both the numerator and the denominator are increased by 2.
Find the fraction.

我定左依2條式
Let x be the denominator
y be the numerator

y-1/x-1 = 1/2 (1)
{
y+2/x+2 = 2/3 (2)

我想係用Substitudetion
但計黎計去都唔對
answer話 the fraction 是4/7
求大家幫下手

回答 (1)

用戶2053

2009-12-06 8:34 am

✔ 最佳答案

(y-1) / (x-1) = 1/2...(1)
(y+2) / (x+2) = 2/3...(2)

(1)交义相乘 :

2(y-1) = (x-1)*1

2y - 2 = x - 1

x = 2y - 1...(3)

代(3)入(2) :

(y+2) / (2y - 1 + 2) = 2/3

3(y + 2) = 2(2y + 1)

3y + 6 = 4y + 2

y = 4,代入(3) :

x = 2*4 - 1 = 7

the fraction 是 y/x = 4/7

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