  Pages: 3 (464 words) / Published: Jul 27th, 2014
A. As a mother is looking at going back to work after staying home with her daughter for the first year she is considering two daycare options. The first option is an in home daycare that charges a flat rate of \$5.00 an hour. The second option is a center-based day care that charges \$185.00 a week based on 40 hours per week, they charge an additional \$8.00 an hour for any time proceeding the 40 hours. The distance to both facilities are very close, making diving distance obsolete. The mother will need to use daycare for 50 hours a week and is trying to determine which option would be cheapest.

B.
Let x represent the total number of hours
Let y represent the total cost of daycare in dollars.

The home based daycare is \$5.00 and hr y = 5x

The center based daycare has a flat rate of \$185.00 for 40 hours a week, and then \$8.00 an hour for any additional hours. for x /< 40 hours y =185 for x > 40 hours y =185+8(x-40)

Home based option y = 5x
Center based option y = 185 (for x /< 40 hours)

Since they are both equal to y, we can use the substitution method to set both equations equal to each other.
5x = 185
5/5 = 185/5 x = 37
Plug x = 37 back into one of the equations above to find y. y = 5 * 37 y= 185
The solution point is 37 hours for \$185, (37,\$185)

Daycare option y = 5x
Center based option y = 185 + 8(x-40) (for x > 40 hours)

Since they are both equal to y, we can use the substitution method to set both equations equal to each other.
5x = 185 + 8(x-40)
5x = 185 + 8x - 320
5x -135 + 8x
-3x = -135 Divide bot sides by 3
-3/3 -135/3 x = 45
Plug x = 45 back into one of the equations above to find y. y = 5 * 45 y = 225
So the solution point is 45 hours for \$225, (45, \$225)
D.
By looking at mathematical reasoning, and comparing each equation on the graph, the mother should easily be able to determine which option makes the most sense