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. solve and then answer Which bowling company will be cheaper to use and when? Use complete sentences. written as a 8th grader and shorten

Answer 1

John is trying to decide between Bowl 360 and Bowler City for his bowling outing. To compare the costs, let's use x to represent the number of hours bowled and y to represent the total cost.

For Bowl 360, there is an initial fee of $10 plus $5 for every hour. So the equation would be y = 10 + 5x.

For Bowler City, there is an initial fee of $20 plus $3 for every hour. So the equation would be y = 20 + 3x.

To determine which bowling alley is cheaper, we can compare the two equations. Let's find the number of hours where both have the same total cost.

Set the two equations equal to each other:
10 + 5x = 20 + 3x

Simplify the equation:
2x = 10

Divide both sides by 2:
x = 5

So, when x is 5 hours, both bowling alleys will have the same total cost.

Now, let's substitute x = 5 into the equations to find the total cost at that point.
For Bowl 360, y = 10 + 5(5) = 10 + 25 = 35.
For Bowler City, y = 20 + 3(5) = 20 + 15 = 35.

At 5 hours, the total cost for both bowling alleys is $35.

Now let's compare. Bowl 360 charges a total of $35 for 5 hours of bowling, while Bowler City also charges $35 for the same timeframe.

Therefore, both bowling alleys will have the same cost at 5 hours.