maths question

Yuk Fun

2008-10-24 8:35 am

The depreciation $C of a car equals to the sum two parts, namely the part varies directly as the number of years n after purchase and the part varies directly as the distance traveled d in km. The depreciation is $36,000 for 2 years after purchase travelling 32000 km and $80,000 for 5 years after purchase travelling 60000 km

a) Express C in terms of n and d

b) Find the depreciation for an identical car for 3 years after purchase and travelling distance of 80000 km

( please give the formula) thank a lots

回答 (1)

老爺子

2008-10-24 9:10 am

✔ 最佳答案

a)

C equal to the sum of two parts:
C = C1 + C2 ...... (1)

The first part varies directly as n:
C1 = k1n ...... (2)

The second part varies directly as d:
C2 = k2d ...... (3)

Put (2) and (3) into (1):
C = k1n + k2d
(where k1 and k2 are proportional constants.)

When n = 2 and d = 32000, C = 36000
36000 = 2k1 + 32000k2
k1 + 16000k2 = 18000 ...... (4)

When n = 5 and d = 60000, C = 80000
80000 = 5k1 + 60000k2
k1 + 12000k2 = 16000 ...... (5)

(4) - (5):
4000k2 = 2000
k2 = 1/2

Put k2 = 1/2 into (5):
k1 + 12000(1/2) = 16000
k1 + 6000 = 16000
k1 = 10000

Hence, C = 10000n + d/2

(b)

When n = 3 and d = 80000:
C = 10000(3) + (80000)/2
C = 30000 + 40000
C = 70000

The depreciation is $70000.
=

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