Question

14. The total monthly cost, $C, of running a
kindergarten with an enrolment of n children
consists of a fixed amount of $5000 and a
variable amount which depends on the
enrolment. For every child enrolled, the
variable amount is $41.
(a) Calculate the total monthly cost of running
the kindergarten if the enrolment is 200.
(b) If the total monthly cost of running the
kindergarten is $20 580, calculate the
number of children attending the
kindergarten.
(c) Write down a formula connecting C and
n.
(d) Sketch the graph of C against n. Is this
relationship a direct proportion between C
and n? Explain.​

Answer 1

Given : The total monthly cost, $C, of running a  kindergarten with an enrolment of n children  consists of a fixed amount of $5000 and a

variable amount which depends on the  enrolment. For every child enrolled, the  variable amount is $41.

To find : Cost if enrolment is 200.

enrolments if cost is $20 580

Draw graph

Solution:

Fixed  Cost  = $ 5000

Variable Cost per enrollment  =   41 $

Students enrolled  =  n

Variable cost  =   41n   $

=> Total Cost C  = 5000 + 41n  $

C  = 5000 + 41n

(a) Calculate the total monthly cost of running  the kindergarten if the enrollment is 200.

=> C = 5000 + 41(200)

=>  C = 5000 + 8200

=> C = 13200 $

(b) If the total monthly cost of running the  kindergarten is $20 580, calculate the  number of children attending the  kindergarten.

=> 20580 = 5000 + 41n

=> 15580 = 41n

=> n = 380

380 enrollments

C  = 5000 + 41n

relationship is not a  direct proportion between C  and n  as there is fixed cost involved

but its a linear  relation

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