High School

Use Gaussian elimination to solve.

The Burkes pay their babysitter $5 per hour before 11 P.M. and $7.50 per hour after 11 P.M. One evening, they went out for 5 hours and paid the sitter $35.00.

What time did they come home?

They came home at ___ A.M.

Answer :

Final answer:

The Burkes paid the babysitter for 1 hour before 11 P.M. and 4 hours after 11 P.M, implying that they came home at 3.00 A.M.

Explanation:

Let's solve the problem using the Gaussian elimination method. If we take babysitter's hours before 11 P.M. as X and the hours after 11 P.M. as Y, we need to solve the two equations derived from the problem description:

  1. 5X + 7.5Y = 35 (the total payment)
  2. X + Y = 5(the total hours of babysitting).

First, multiply the second equation by -5 and add the resulting equation to the first one to cancel out X, i.e.,-5X - 5Y = -25. Then, add up the two equations to get 2.5Y = 10 (Gaussian elimination), so Y = 10 / 2.5 = 4. To find X, substitute Y back into the second equation: X = 5 - Y = 1. Therefore, the Burkes paid the sitter for 1 hour before 11 P.M. and 4 hours after. So, they came back at 11 P.M. + 4 hours = 3.00 A.M.

Learn more about Gaussian Elimination here:

https://brainly.com/question/30400788

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