F.4 Maths

2011-12-18 1:53 am
某車去年的價值是兩年前的r%,現時的價值是去年的(r-5)%。若該車現時的價值是兩年前的68%,求r的值。

回答 (2)

2011-12-18 2:20 am
✔ 最佳答案
設2年前車子的價值是x﹐則現在的價值是0.68x

據題意0.68x = x * r% * (r - 5)%

0.68 = r(r - 5)/100^2

6800 = r(r - 5)

r = 85
2011-12-18 2:26 am
let P be the price 2 years ago
last year: L = P(r%)
now: N = L(r-5)% = P(r%)(r-5)% = P(68%)
(r%)(r-5)% = 68%
(r/100) [(r-5)/100] = 68/100
r [(r-5)/100] = 68
r^2 - 5r = 6800
r^2 - 5r - 6800 = 0
(r-85)(r+80) = 0
r = 85 or -80 (neglected)


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