John is deciding which bowling alley to choose from. Bowl 360 charges an initial fee of $10 with a rate of $5 every hour. Bowler City charges an initial fee of $20 with a rate of $3 every hour. Let x represent hours, while y represents total cost. 1. What does the point (5, 35) represent in this context? 2. Which bowling company will be cheaper to use and when? Use complete sentences.

Answer 1

1. The point (5, 35) represents the total cost for using Bowl 360 for 5 hours. At Bowl 360, there is an initial fee of $10 and a rate of $5 per hour. Therefore, after 5 hours, the total cost would be 10 + (5 * 5) = 35.

2. To determine which bowling company will be cheaper to use and when, we need to compare the cost equations for both companies.

For Bowl 360, the cost equation is y = 5x + 10.
For Bowler City, the cost equation is y = 3x + 20.

To find when Bowl 360 will be cheaper, we need to set their cost equations equal to each other and solve for x:

5x + 10 = 3x + 20
2x = 10
x = 5

So, for 5 hours or fewer, Bowl 360 will be cheaper to use.

To find when Bowler City will be cheaper, we can compare their cost equations for x > 5. At x = 6, the respective costs are:
- Bowl 360: 5*6 + 10 = 40
- Bowler City: 3*6 + 20 = 38

Therefore, starting from 6 hours, Bowler City will be cheaper to use.