Jada has a job with the city’s Parks and Recreation Department. She receives an hourly wage plus time and a half for any hours over 40 worked each week.

Which piecewise-defined function best models her weekly pay h(t) if she works t hours and receives an hourly wage of $12?

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jtellezd jtellezd · Answer 1 · 2021-10-25T14:09:47+02:00

As per the problem statement, there is a linear relation, between de whole earnings of Jada, and her working time.

Solution:

y = 240 + 6×t

A Linear relation is of the form:

y = ax + b

If we call total earnings´Jada "y", and "t" the whole quantity of worked hours per week, we get:

a fixed amount working 40 hours 12×40 = 480 $

and the quantity over 40 hours as ( t - 40 ) × 6.

Then y = fixed quantity + overtime

y = 480 + ( t - 40 ) × 6 reordering this expression

y = 480 + 6×t - 240

y = 240 + 6×t

Just for checking, if this equation satisfies, the conditions of the problem

if t = 40 h that means she did´nt do any overtime,

she earns y = 240 + 6×(40) ⇒ y = 480 $

if t = 50 h meaning 10 hours of overtime, she earns:

y = 240 + (50)×6 ⇒ y = 540 $

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