Question

The table shows the cost, C, in dollars, to rent a car from Carl's Car Rentals. Determine the following: a) What is the fixed cost? b) What is the variable cost? c) Write an equation relating your answer from part (a) and part (b) [be sure to use the variables stated in the table]. d) What kind of variation is this relationship showing? e) Calculate the cost of renting a car for a day and driving a total of 800km.

Answer 1

a) Fixed cost = $50

b) Total variable cost is $15, while variable cost per unit is $0.15.

c) C = 50 + d0.15

d) Direct variation

e) The cost of renting a car for a day and driving a total of 800km is $170,

Explanation:

a) What is the fixed cost?

Fixed cost is a cost that does not change with the level of activity. Fixed is incurred whether there is an activity, or there is no activity at all, that is, when the activity is zero.

Since cost, C, is equal to $50 when distance, d (km), is equal to zero in the table, the fixed cost is therefore equal to $50, i.e.:

Fixed cost = $50

b) What is the variable cost?

Variable cost is a cost that changes as the level of activity changes. From the table, the variable cost can be obtained by deducting the fixed cost from the total cost. This can be calculated using any of the distance, d (km), in the table.

Using the distance of 100 as an example, the total variable cost can be obtained as follows:

Variable cost = Total Cost at 100 distance - Fixed cost = $65 - $50 = $15

Note that variable cost per distance at 100 distance can be obtained as follows:

Variable cost per distance = $15 / 100 = $0.15

c) Write an equation relating your answer from part (a) and part (b)

Since,

C = Cost

d = distance (km)

Fixed cost = $50

Variable cost per distance = $0.15

Therefore, suppressing the dollar sign for simplicity purpose, an equation relating the above can be given as follows:

C = 50 + d0.15 ............................................. (1)

d) What kind of variation is this relationship showing?

This is a direct variation.

Direct variation is a variation in which an increase in one variable will lead to an increase in another variable.

For example in equation (1), a increase in d which is multiplied by $0.15 will lead to an increase in C.

e) Calculate the cost of renting a car for a day and driving a total of 800km.

This implies that d = 800.

Substituting d = 800 into equation (1), we have:

C = 50 + (800 * 0.15) = 170

Therefore, the cost of renting a car for a day and driving a total of 800km is $170.