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. with this context Which bowling company will be cheaper to use and when? Use complete sentences.
To determine which bowling alley is cheaper to use, we need to compare the total cost for a given number of hours.
For Bowl 360, the total cost (y) can be represented by the equation y = 5x + 10, where x is the number of hours played.
For Bowler City, the total cost (y) can be represented by the equation y = 3x + 20.
To find out when one bowling alley will be cheaper than the other, we need to set up an inequality.
We can set up the inequality 5x + 10 < 3x + 20 to compare the costs.
Simplifying the inequality gives us 2x < 10.
Dividing both sides of the inequality by 2, we get x < 5.
This means that if John plans to play for less than 5 hours, Bowler City will be cheaper. However, if John plans to bowl for 5 hours or more, Bowl 360 will become cheaper.