Question

You and your friends want to go to a skate park on Saturday. There are two amazing parks in your neighborhood...Sam‛s Skate Park, and Brad‛s Skate Park. The parks both charge for skating. Each park's price is described below. Sam‛s Skate Park: $3 to get into the park and $1 for every hour of skating. Brad‛s Skate Park: $5 to get into the park and $0.50 for every hour of skating. Sam‛s Skate Park equation: ______________ Brad‛s Skate Park equation: ______________ Click here to graph your system. Answer the following questions after graphing your equations:

1. What are your two equations for this system?
2. What does the x and y represent in your equations?
3. Where do the two lines intersect?
4. What does this intersection mean?
5. Which skate park has the best deal if you plan on skating for 3 hours? Explain why you chose this park.

Answer 1

1. 1st gap: y=(3+x)

2nd gap: y=(5+0.5x)

2. x is the number of hours you and your friends skate in Sam‛s Skate Park or in Brad‛s Skate Park and y is the total price of skating.

3. 4 hours

4. The total prices in two parks are equal when skating for 4 hours.

5. Sam's Skate Park has the best deal.

Explanation:

Let x be the number of hours you and your friends skate in Sam‛s Skate Park or in Brad‛s Skate Park and y be the total price of skating.

Sam‛s Skate Park: $3 to get into the park and $1 for every hour of skating, then the price is $1·x for x hours and y=(3+x) in total.

Brad‛s Skate Park: $5 to get into the park and $0.50 for every hour of skating, then $0.5·x for x hours and y=(5+0.5x) in total.

1. 1st gap: y=(3+x)

2nd gap: y=(5+0.5x)

2. x is the number of hours you and your friends skate in Sam‛s Skate Park or in Brad‛s Skate Park and y is the total price of skating.

3. Equate both expressions:

3+x=5+0.5x,

x-0.5x=5-3,

0.5x=2,

5x=20,

x=4.

4. The total prices in two parks are equal when skating for 4 hours.

5. Sam's Skate Park price for 3 hours is $(3+3)=$6 and Brad's Skate Park price for 3 hours is $(5+3·0.5)=$6.5. Sam's Skate Park has the best deal, because $6<$6.5.