Question

You want to go to the skate park, and you have two options:

Sami's Skate Park: $6 to get into the park and $2.00 for every hour.
Brad's Skate Park: $10 to get into the park and $1.00 for every hour.
How long until the two parks would have the same total cost? What is that total cost?

1- DEFINE THE VARIABLES:

2- SHOW YOUR WORK TO SOLVE HERE:

3- EQUATIONS:

4- QUESTIONS:

5- When are the costs the same?

i) when are the cost the same?
___ hours

ii) What is that cost?___$.

Answer 1

See Explanation

Explanation:

Define the variables

Let the entry fee be c and the hourly rate be m

Let the number of hours be x and the total amount be y

Work to solve

For Sami's skate

`c = 6` and
`m = 2`

For Brad's skate

`c =10` and
`m = 1`

The equations

The equation is derived using:
`y = mx + c`

For Sami's skate

`y = 2x + 6`

For Brad's skate

`y = x + 10`

When the cost are the same

To do this, we equate both expressions

i.e.

`y = y`

`2x + 6 = x + 10`

`2x -x = 10 - 6`

`x = 4`

i.e. the cost are the same at the 4th hour

What is the cost

Substitute 4 for x in any of the equations

`y = x + 10`

`y = 4 + 10`

`y = 14`

The cost is $14.00