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14. (a). The cost C of manning household is partly constant and partly varies as the number of people n, in the house. For 8 people, the cost is ¢70,000 and for 10 people, the coast is $90,000, find i. An expression for C in terms of n ii. The weekly cost for 12 people​

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Answer:

C = 10000n - 10000 ;

$110,000

Step-by-step explanation:

Given :

Cost = C

C partly varies as n ; C α n ; C = k1 * n = k1n

C partly constant = k2

Hence,

C = k1n + k2

For n = 8 ; C = 70000

For n = 10 ; C = 90000

8k1 + k2 = 70000 - - - - - (1)

10k1 + k2 = 90000 - - - - (2)

Subtract 1 from 2

8k1 - 10k1 = 70000 - 90000

-2k1 = - 20000

k1 = 10000

Put k1 = 10000 in (1)

8(10000) + k2 = 70000

80000 + k2 = 70000

k2 = 70000 - 80000

k2 = - 10000

The expression :

C = 10000n - 10000

Weekly cost for 12 people :

n = 12

C = 10000(12) - 10000

C = 120000 - 10000

C = $110,000

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