Qlt Task 5

Part A: The Smith family is looking for childcare for their young son. They are considering two different options. The first option is a home-based option that charges $200 per week regardless of how many hours the child is there. The second is a center-based option that charges $150 per week for the first 25 hours, each hour after that is $10. Right now both Mr. and Mrs. Smith are working 40 hours a week, however Mrs. Smith is hoping to start working only 25 hours per week. What is the most cost effective for their situation now? And, what would be more cost effective if Mrs. Smith were to start working 25 hours per week?

Part B: The cost will be represented by y, and the number of hours will be represented by x.

1. Home Based Option: y=200

Center Based Option: y=10(x-25) +150 OR y=150.

2. The Home Based equation is written as y=200 because it is a flat rate fee. No matter the hours the child attends it will always cost $200, therefore y=200.

The Center Based Option has 2 equations. The first one y=10(x-25)+150. This equation would be used if Mrs. Smith continues to work full time. The 10 represents the cost per hour after 25 hours. X represents the total number of hours Mrs. Smith needs for child care so for full time would be 40. Since the cost of 25 hours is represented by the 150 on the outside of the parentheses we subtract 25 hours from the total number of hours (x).

The second equation would be used if Mrs. Smith decides to only work 25 hours per week. Since the first $150 covers child care up to 25 hours per week, the equation would simply be y=150.

3. For the Home Based Option there is no equation to solve. It is simply y=200.

In order to solve the equation y=10(x-25)+150 we need to solve for x. To solve for x, we need to set the equations equal to each...