Question

Steven earns extra money babysitting. He charges $24.75 for 3 hours and $66.00 for 8 hours. Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.

Answer 1

To represent the relationship between the number of hours Steven babysits (x) and the amount he charges (y), we can set up a piecewise equation based on the given information:

For x ≤ 3 hours:
y = 24.75

For 3 < x ≤ 8 hours:
y = mx + b

Where m is the slope (rate per hour) and b is the y-intercept (the amount charged for 3 hours).

To determine the slope, we can use the information provided for 8 hours. We can calculate the rate per hour by dividing the change in the amount charged by the change in the number of hours:

m = (66.00 - 24.75) / (8 - 3)

Now, substituting the values into the equation:

For 3 < x ≤ 8 hours:
y = [(66.00 - 24.75) / (8 - 3)]x + 24.75

This equation represents the relationship between the number of hours Steven babysits (x) and the corresponding amount he charges (y) for hours beyond 3 up to 8. For 3 hours or less, the charge remains constant at $24.75.

Answer 2

Explanation:

Let x represent the number of hours Steven babysits and y represent the amount he charges.

$24.75 for 3 hours

⇒ for 1 hour 24.75/3 = 8.25/hour

similarly $66.00 for 8 hours

⇒ for 1 hour 66/8 = 8.25/hour

He charger 8.25 per hour

So, for x hours, the amount y is :

y = 8.25x