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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?

Respuesta :

calculista

Answer:

Part a) [tex]y=18.50x+100[/tex]

Part b) The total cost is [tex]\$220.25[/tex]

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

[tex]y=mx+b[/tex]

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

[tex]m=\$18.50\ per\ hour[/tex]

The y-intercept or initial value is equal to

[tex]b=\$100[/tex]

substitute

[tex]y=18.50x+100[/tex]

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

[tex]y=18.50(6.5)+100[/tex]

[tex]y=\$220.25[/tex]

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

we have that

[tex]y=220.25[/tex]

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

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