a school organizes a pinic for students.the total expenditure consists of two parts.the first part is the cost of hiring coaches and the second part is the cost of food.a coach can carry 40 participants and the cost of hiringis a constant.while the cost of food varies directly as the number of participants.if there are 60 participants,the total expanditure is $3800.if there are 120 participants,the total expenditure is $7200.
a)find the cost of hiring a coach and the cost of food per participant.
b)if there are 135 participants,find the total expenditure.
variation
2010-09-22 7:00 am
回答 (1)
2010-09-22 8:12 am
✔ 最佳答案
a)$T = total expenditure (variable)
n = number of participants (variable)
c = number of coaches hired (variable)
$k = cost of food per participant (constant)
$k' = cost of hiring a coach (constant)
T = k'c + kn
When n = 60 and T = 3800:
c = 60/40 = 2 (round up to nearest integer)
3800 = k'(2) + k(60)
2k' + 60k = 3800
k' + 30k = 1900 …… (1)
When n = 120 and T = 7200:
c = 120/30 = 3
7200 = k'(3) + k(120)
3k' + 120k = 7200
k' + 40k = 2400 …… (2)
(2) - (1):
10k = 500
k = 50
Put k = 50 into (1):
k' + 30(50) = 1900
k' = 400
Cost of hiring a coach = $400
Cost of food poer participant = $50
b)
T = 400c + 50n
When n = 135:
c = 135/40 = 4 (rounded up to nearest integer)
T = 400(4) + 135(50) = 8350
Total expenditure = $8350
參考: adam
收錄日期: 2021-04-16 11:39:09
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