數學問題 (急!)

1.The weights of copper and zinc of an alloy are in the ratio15:13. Find the weight of copper in 140kg of alloy.
Let the weight of copper is x kg.
Let the weight of zinc is 140-x kg.
As copper to zinc ratio = 15:13, so
x/(140-x) = 15/13
15(140-x) = 13x
2100 - 15x = 13x
28x = 2100
x = 75
So the weight of copper is 75 kg.
==================================
2. A cake is devided into two parts in the ratio 4:1 .The smaller part is further divided into two parts in the ratio 3:2 .If the smallest part of the cake weighs 100g, find the weight of the whole cake.
Let the weight of the whole cake be x g.
The larger part
= x * [4/(4+1)]
= x * 4/5
= 4x/5
The smaller part
= x * [1/(4+1)]
= x * 1/5
= x/5 ................. (1)
The smaller part is subdivided into 3:2
The smallest part (the smaller part of the smaller part)
= the smaller part * [2/(3+2)}
= the smaller part * 2/5
= x/5 * 2/5 ............. by (1)
= 2x/25
As the smallest part is 100g, so
100 = 2x/25
2500 = 2x
x = 1250
So the weight of the whole cake is 1250 g.

==================================
Proportion
　x 3
----- = ---
x - 2 4

Assume x-2 != 0, i.e. x != 2
　x 3
----- = ---
x - 2 4
4x = 3(x-2)
4x = 3x-6
x = -6
So x = -6.

2006-12-01 13:28:58 補充：
小小補充：第三題有亂碼，應該是　x 3----- = ---x - 2 4Assume x-2 != 0, i.e. x != 2　x 3----- = ---x - 2 44x = 3(x-2)4x = 3x-6x = -6So x = -6.

2006-12-01 13:31:42 補充：
再補充：比例題目中，如果將一個整體 c 分成 a，b 兩份，而比例分別為 x:y。公式為：a = c * x/(x+y)b = c * y/(x+y)意思是分母取 x+y，而 a 是 x+y 中的 x 份，b 是 x+y 中的 y 份。

(1).

Copper = 140kg * [15 / (15 + 13)]
= 140kg * [15 / 28]
= 75kg

Further reference:

Zinc = 140kg * [13 / (15 + 13)]
= 140kg * [13 / 28]
= 65kg

Zinc = 140kg – 75kg
= 65kg

(2).

The smallest part = 100g

The smaller part of the cake = 100 / 2 * (3+2)
= 250g

The weight of the whole cake = 250 / 1 * (4+1)
= 1,250g

(3).

x / (x – 2) = 3/4

[x / (x – 2)] * 4 = 3/4 * 4

[x / (x – 2)] * 4 = 3

4x / (x – 2) = 3

4x = 3 (x – 2)

4x = 3x – 6

4x - 3x = -6

x = -6