Question

The total expenses of a conference are partly constant and partly vary directly as the number
of participants. When there are 50 participants, the total expenses are $10100. When there are
10 participants, the total expenses are $2100.

Answer 1

The total expense and the number of participants is a linear function that

has the fixed expense value as the y-intercept.

The expense per participants, X is $200

The fixed expense is $100

Reasons:

Let C represent the constant expenses and let X represent the part that

varies with the number of participants, we have;

10,100 = 50·X + C...(1)

2,100 = 10·X + C...(2)

Subtracting the second equation from the first, gives;

10,100 - 2,100 = (50·X + C) - (10·X + C) = 40·X

8,000 = 40·X

$X = \dfrac{8,000}{40} = 200$

The cost per participant, X = $200

From equation (2), we get;

2,100 = 10·X + C

Therefore;

2,100 = 10 × 200 + C

C = 2,100 - 10 × 200 = 100

The fixed cost, C = $100

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