Question

Steven Scarecrow is looking to go on a Haunted Hayride but wants to leave the kids at home with a babysitter. He found that Casper charges $23 plus $2 per hour and Balthazar charges $15 plus $4 per hour. Write and solve an equation to determine the number of hours that Steven Scarecrow could hire either babysitter for the same cost.

Answer 1

Steven Scarecrow could hire either babysitter for the same cost if he hires them for 4 hours, by setting up and solving the equations for each babysitter's charges equal to each other.

Step-by-step explanation:

The question asks for an equation to determine the number of hours Steven Scarecrow could hire either babysitter for the same cost. To find this, we need to set the cost of hiring Casper equal to the cost of hiring Balthazar and solve for the number of hours.

Let x represent the number of hours. For Casper, the cost will be $23 (the flat rate) plus $2 per hour, which gives us an equation C(x) = 23 + 2x. For Balthazar, the cost will be $15 (the flat rate) plus $4 per hour, resulting in an equation B(x) = 15 + 4x.

To find when the costs are equal, we set the two equations equal to each other:

23 + 2x = 15 + 4x

Solving this equation for x:
Subtract 2x from both sides to get 23 = 15 + 2x

Subtract 15 from both sides to get 8 = 2x

Divide both sides by 2 to get x = 4

Therefore, Steven Scarecrow could hire either babysitter for the same cost if he hires them for 4 hours.