F3 maths!!~~有2 question,,,快快,thx!!!!!

18) The weight of copper is:
40kg x 75% = 30kg

The weight of tin is:
40kg x 25% = 10kg

After adding 10kg tin to the alloy, the weight of copper and tin will be:
30 kg and 20kg(10 10kg) respectively. (The alloy becomes 50 kg)

Therefore, the new % of copper and tin in the alloy by weight will be:
30/50x100% : 20/50x100%
60% : 40%



20) Let the price of gasoline be X, the consumption of gasoline be Y1(before change of price) & Y2 (after change of price) and the expenditure be Z


(三者之關係即：） X x Y1 = Z (Y1即=Z/X)
或 1.2X x Y2 = Z (Y2即=Z/1.2X)


Change of Y is:
Y1-Y2 = Z/X - Z/ 1.2X
Y1-Y2 = Z/X - Z/ 1.2X
Y1-Y2 = 0.2 Z/ 1.2X (註：把0.2跟1.2約掉 = 1/6）
Y1-Y2 = 1/6 (Z/X) （註：Z/X = Y1)

所以gasoline 的 consumption應該為減少六分一，才能保持總額不變




如不太明白，可試代入數字看看：

試代入：
　　 X=$10, Z= $240
$10 x Y（加價前） = $240
　　　　Y（加價前）＝24L

If X increased be 20%,
($10 x 120%) x Y （加價後）= $240
$12 x Y（加價後） = $240
　　　　 Y（加價後） ＝20L


The % change in the consumption of gasoline should be:
(24-20)/24 = 1/6

Therefore, % change should be around -16.7%



（很久沒有做數學家課，不記得列式方法了，只希望上面的解釋能幫助你去明白）

18)
Weight of copper in original alloy
=75% (40)
=30kg
Weight of tin in original alloy
=40-30
=10kg

Percentage of copper in new alloy
=30/(40+10) x 100%
=60%
Percentage of tin in new alloy
=100-60
=40%

20) (this method is quite troublesome)
Let x be the original price of gasoline, y be the consumption and z be the percentage change of consumption.
xy=(1.2x)[(1-z)y]
y=1.2(1-z)(y)
1/1.2=(1-z)
z=1.67 (correct to 3 sig. fig.)
.'. The percentage change in the consumption of gasoline is 16.7%