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

Answer:

Part a) $y=18.50x+100$

Part b) The total cost is $\ 220.25$

Part c) see the explanation

Step-by-step 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