Question

The total cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60 , where X is the number of ski trip you take. a) solve the question for x b) How many ski trips do you take if you spend a total of $315? How about $485?

Answer 1

We have a cost function C that depends on the number of ski trips (expressed with the variable x).

a) We have to solve for x.

This means, find an explicit expression for x in function of C.

We can start from C(x) and rearrange it as:

`\begin{gathered} C=85x+60 \\ C-60=85x \\ (C-60)/(85)=x \\ x=(1)/(85)(C-60) \end{gathered}`

NOTE: we can rearrange the equation for x in different forms, but this one make it easier to solve the problems for b.

b) We can use the last result to find the number of ski trips that correspond to a total cost of $315. To do that we replace C with 315 and calculate x:

`x=(1)/(85)(315-60)=(1)/(85)(255)=3`

For C = $485 we can calculate x as:

`x=(1)/(85)(485-60)=(1)/(85)(425)=5`

Answer:

a) An expression for x in function of C is x = (C - 60)/85.

b) For a cost of $315, we have 3 ski trips.

For a cost of $485, we have 5 ski trips.