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Question

The monthly fee $P for a mobile phone service plan is the sum of two parts. One part is the basic fee $C which includes a basic airtime of $800 minutes, another part varies directly as the additional airtime. The following are the airtime and monthly fee of two customers. Let n minutes be the airtime where n >= 800.

Customer Airtime(n minutes) Monthly fee $P

Jack 830 84

May 950 108

(a) Express P is terms of n.

(b) If the airtime of Doris is 1135 minutes, what is her monthly fee?

Answer 1

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(a)

Assume P = C + a (n -800)

From Jack,

84 = C + a(830 - 800)

84 = C + 30a .... (1)

From May

108 = C + a(950 - 800)

108 = C + 150a ... (2)

(2) - (1)

24 = 120a

a = 0.2 ... (3)

Put (3) into (1)

84 = C + 30 x 0.2

C = 78

Therefore, P = 78 + 0.2(n - 800)

(b) For n = 1135,

P = 78 + 0.2(1135 - 800)

P = 78 + 67

P = 145

Ans. Doris monthly fee is $145.