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.
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.