Question

You plan to go skiing this weekend in Tennessee. The ski resort charges $18.50 per hour in addition to a $100 deposit to rent skis.

a) Write a linear equation to represent this situation.

b) Use the equation to find the total cost to rent skis from 8:30 am to 3:00 pm. You must show and explain all your work.

c) What does your answer mean in context of the problem?

Answer 1

Part a)
`y=18.50x+100`

Part b) The total cost is
`\$220.25`

Part c) see the explanation

Explanation:

Part a) Write a linear equation to represent this situation

Define the variables

Let

x ----> the number of hours

y ----> the total cost in dollars

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or the unit rate

b is the y-intercept or initial value (value of y when the value of x is equal to zero)

In this problem we have that

The unit rate or slope is equal to

`m=\$18.50\ per\ hour`

The y-intercept or initial value is equal to

`b=\$100`

substitute

`y=18.50x+100`

Part b) Use the equation to find the total cost to rent skis from 8:30 am to 3:00 pm

Remember that

3:00 pm=15:00

so

from 8:30 am to 3:00 pm, the total hours is equal to

15:00 -8:30=6:30=6.5 h

For x=6.5 h

substitute in the linear equation and solve for y

`y=18.50(6.5)+100\\y=\$220.25`

Part c) What does your answer mean in context of the problem?

we have that

`y=220.25`

That means -----> The total cost to rent skis for 6.5 hours is equal to $220.25