Mathematics Questions! Help !

好欣賞你問問題都註明出處！　：）

1) The base (底) and the height (高) of a parallelogram (平行四邊形) are both decreased by 10%. Find the percentage change in the area (面積) of the parallelogram.

可以這樣分析。
Let b and h be respectively the original base and height of the parallelogram.
The original area is A = bh.
Now both b and h are decreased by 10%, that means the base and the height now become 0.9b and 0.9h.
The new area is A' = (0.9b)(0.9h) = 0.81 bh = 0.81A
Therefore, the change in area of the parallelogram is
(A' - A)/A * 100% = (0.81A-A)/A * 100% = (0.81-1)/1*100% = -19%

2) An alloy (合金) weighing 400 g is made up of 80% copper (銅) by weight. If 100 g copper is added to the alloy, what will be
(a) the percentage of copper by weight in the new alloy
Originally, the weight of copper in the alloy is 400*80% = 320 g.
Now, after adding 100 g of copper, the total weight of copper is 320 + 100 = 420 g.
The weight of the new alloy is 400 + 100 = 500 g.
Therefore, the percentage of copper by weight in the new alloy is 420/500*100% = 84%
(b) the percentage change in the proportion of copper by weight in the alloy
From the question, the original proportion of copper in the alloy is 80%.
From part (a), the new proportion of copper in the alloy is 84%.
As a result, the percentage change in the proportion of copper by weight in the alloy is (84%-80%)/(80%)*100% = (84-80)/80*100% = 5%

以上我故意寫得詳細一點，因為有時候數學題除了著重計算過程之外，表達的方式都很重要，所以借這個機會讓你試下閱讀較為詳盡的寫法。

1 ) The base and the height of a parallelogram are both decreased by 10% . Find the percentage change in the area of the parallelogram

Let both the original base and height of the parallelogram be 1cm.
Original area=1x1=1
New area =(1+10%)(1+10%)
= 1.21
percentage change =[(1.21-1)/1]x100%
=21%
∴area is increased by 21%


2 ) An alloy weighing 400 g is made up of 80 % copper by weight . If 100 g copper is added to the alloy , what will be
(a) the percentage of copper by weight in the new alloy
(b) the percentage change in the proportion of copper by weight in the alloy

(a) Percentage of copper =[(400x80%+100)/500]x100%
=[420/500]x100%
=84%

(b) percentage change =[(84%-80%)/80%]x100%
=(4%/80%)x100%
=5%
∴proportion will increased by 5%

2013-08-17 05:42:44 補充：
decreased 睇錯 increased:(