1.如果汽油的價格上漲20%,用戶必須多節省百分之幾的耗油量才能令支出維持不變?
2.李太太有一筆銀行存款。若年利率由4%減至3.75%,則他每年的單利息會減少$25 000,求本金。
2006-10-23 12:20:04 · 4 個解答 · 發問者 Anonymous in 科學 ➔ 數學
1.
設原來汽油的價格 = X , 原來耗油量 = Y
原來支出 = XY
要令支出維持不變,
[設用戶必須多節省a % 的耗油量]
( 1 + 20%) X * ( 1 - a % ) Y = XY
1.2X * (1 - a% ) Y = XY
(1 - a %)Y = 5 / 6 Y
Therefore
1 - a% = 5 / 6
1 - a % = 0.8333...
a = 16.666... = 16 . 67 (corr . to 2d.p.)
用戶必須多節省百分之16.67耗油量才能令支出維持不變
2
設本金 = $ x,時期 = 1
x* 4% - x * 3.75% = 25000
0.25%x = 25000
x = 10,000,000
本金 = $ 10,000,000
2006-10-23 12:35:59 · answer #1 · answered by J 7 · 0⤊ 0⤋
1. (1.2-1)除1.2乘100%
=16.7%
2. 25000除(4%-3.75%)
=100000
2006-10-23 15:21:29 · answer #2 · answered by Tsz Chung 1 · 0⤊ 0⤋
1. because 支出=汽油的價格x耗油量
so, if 支出維持不變 and 汽油的價格上漲20%,
then耗油量必須節省
Let x=支出, y=汽油的價格, z=耗油量
then x=yz
let a=汽油的價格上漲20%, b=new耗油量
then x=ab
and a=(1+20%)y=1.2y
because x=yz=ab
yz=ab
yz=1.2yb
z=1.2b
b=z/1.2
=0.8333333z or 83 1/3%z
so 節省的耗油量=z-b
=z-83 1/3%z
=16 2/3%z
so 節省:16 2/3%
2. Let x=本金
x(1+4%)-x(1+3.75%)=25 000
0.25%x=25000
x=10000000
so 本金is$10000000
2006-10-23 12:57:41 · answer #3 · answered by ? 3 · 0⤊ 0⤋
1.16.6%
2.$10 000 000
2006-10-23 12:36:09 · answer #4 · answered by ? 1 · 0⤊ 0⤋