數學(Variations)

It is not a ecnomic problem but a mathematic one.

Let the expense be E, and the number of guest be G.
∵the expenses are partly constant and partly vary directly as the number of guests.
∴E = k1 + (k2)G, where k1 and k2 are constants.

When there are 50 guests, the expenses is $1850.
1850 = k1 + (50)(k2)----------------------(1)

When there are 150 guests, the expenses are $4350.
4350 = k1 + (150)(k2)---------------------(2)

(2)-(1):
4350-1850 = (150-50)(k2)
2500 = 100k2
k2 = 25

Put k2 = 25 into (1)
1850 = k1 + (50)(25)
k1 = 600

∴E = 600 + 25G

Put 200 into G:
E = 600 + (25)(200)
E = 5600
∴The cost when there are 200 guests is $5000

1850 :50 37:1
4350:150 29:1
EXPENSE = 可變成本 (v)+ 固定成本(f)
50v + f = 1850 (i)
150v +f = 4350 (ii)
(ii) - (i)
100v=2500
v = 25
50 (25) + f = 1850
f = 600
答案
200 (25) + 600 =5600
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