Problema Solution
The Houlihans pay their babysitter $5 per hour before 11 pm and $7.50 per hour after 11 pm. One evening they went out for 5 hours and paid the babysitter $30. What time did they come home?
Use Gaussian elimination or Gauss-Jordan elimination to solve.
Answer provided by our tutors
let
x = the number of hours before 11 pm
y = the number of hours after 11 pm
One evening they went out for 5 hours and paid the babysitter $30
x + y = 5
5x + 7.50y = 30
we need to solve the system of equations
x + y = 5
5x + 7.50y = 30
the first thing to do is to get rid of the leading x-terms in two of the rows. So I'll multiply the first row by -5, and add it to the second row
x + y = 5
-5x - 5y + 5x + 7.50y = -25 + 30
we get
x + y = 5
2.50y = 5
x + y = 5
y = 5/2.50
x + y = 5
y = 2
x + 2 = 5
y = 2
x = 5 - 2
y = 2
x = 3
y = 2
2 hours after 11 pm is 1 am so they came home at 1 am.