急! F5 about equations 1Cq02

20.
Let v km/h be Jack's original cycling speed.

(30/v) - [30/(v + 3)] = 1/2
[30(v + 3) - 30v] / [v(v + 3)] = 1/2
90/(v² + 3v) = 1/2
v² + 3v - 180 = 0
(v - 12)(v + 15) = 0
v = 12 or v = -15(rejected)

Jack's original cycling speed = 12 km/h


21.
(a)
Let n be the number of glassware bought by the students originally.

(n - 2)[(48/n) + 3] - 48 = 22
(n - 2)[(48/n) + 3] = 70
(n - 2)[(48/n) + 3]n= 70n
(n - 2)(48 + 3n)= 70n
3n² - 28n - 96 = 0
(n - 12)(3n + 8) = 0
n = 12 or n - -8/3(rejected)

Number of glassware bought by the students originally = 12


22.
20000 x (1 - 36%)^t - 11000 x (1 - 20%)^t = 3000
20000 x 0.64^t - 11000 x 0.8^t = 3000
20000 x 0.8^2t - 11000 x 0.8^t = 3000

Let u = 0.8^t
20000u^2 - 11000u = 3000
20u^2 - 11u - 3 = 0
(4u - 3)(5u + 1) = 0
u = 3/4 or u = -1/5(rejected)

0.8^t = 0.75
t = log0.75/log0.8
t = 1.289

2012-08-16 22:13:18 補充：
2.(b)
Selling price of each piece of glassware
= $[(48/12) + 3]
= $7 ...... (ans)