about variations. 20points thx

2012-03-24 8:26 pm
for the first hour, the parking fee $C of a van in car park X is $A. thereafter, the fee $B varies directly as the parking time on a half-hourly basis. when a van is parked in car park X for 3 hours, the parking fee is $68; when a van is parked for 4 hours, the parking fee is $92. assume that a van has been parked in car park X for n hours where n ≥ 1.

a) (i) express B in terms of n.
(ii) express C in terms of n.

b) if a van has been parked in car park X for 10 hours, how much is the parking fee?

c) for car park Y, the parking fee $F of a van varies directly as the parking time on a half-hours basis. when a van is parked in car park Y for 6 hours, the parking fee is $120. After how long should the van be parked at least such that the parking fee charged by car park X will be higher than that charged by car park Y?
更新1:

please include the step. thanks a lot! the answer should be: a) (i)B = 24(n-1) (ii) C = 24n-4 b) $236 c) 1 hours thankssssss!

回答 (2)

2012-03-24 9:10 pm
✔ 最佳答案
ai)Let C = A + B = A + k(n-1)/0.5 = A + 2k(n-1) 68 = A + 2k(3-1) ......(1)
{
92 = A + 2k(4-1) ......(2)(2) - (1) :92 - 68 = 6k - 4k
k = 12So B = 2k(n-1) = 24(n-1)ii)Sub. k = 12 into (1) :
68 = A + 12 * 4
A = 20 So C = A + B = 20 + 24(n-1) = 24n - 4

b)By a) : C = 24n - 4 Put n = 10 , C = 240 - 4 = $ 236

c)Let F = K (n / 0.5) = 2Kn ,
when n = 6 ,
F = 120 = 12K
K = 10So F = 20nC > F
24n - 4 > 20n
4n > 4
n > 1At least 1 hours.
2012-03-24 10:30 pm
Part c)

n > 1

It takes at least 1.5 hours.
The given answer (1 hours) is INCORRECT.


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