# QLT1 Task 5

**Topics:**Elementary algebra, Harshad number, Equals sign, Time /

**Pages:**3 (464 words) /

**Published:**Jul 27th, 2014

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