Question

An engineering technician makes $25 an hour for the first 40 hours she works during a week and $32 an hour for each hour over 40 hours. Which piece wise equation models her total weekly pay y in dollars as in relates to the number of hours x that she has worked during the week

Answer 1

Pay = $y
Hours work = x
Addition amount paid for over 40 hours = 32 -2 5 = 7

y = 25x + 7(x - 40)

Answer 2

`y=\left\{\begin{matrix}25x; & 0\leq x\leq 40\\ 1000 + 32(x-40); & x > 40\end{matrix}\right.`

Explanation:

Here, x represents the number of hours she worked and y represents the total pay in dollars for x hours,

∵ She earns $25 an hour for the first 40 hours,

i.e. y = 25x if x ≤ 40,

Hours can not be negative,

⇒ y = 25x if 0 ≤ x ≤ 40,

Also, she earns $32 an hour for each hour over 40 hours.

i.e. y = earning for 40 hours( with the rate of $ 25 per hour) + earning for each hours exceeded 40 hours ( with the rate of $ 32 per hour ),

Thus, if x > 40,

y = 25 × 40 + 32 × ( x - 40 )

⇒ y = 1000 + 32(x - 40)

Hence, the required piece wise function would be,

`y=\left\{\begin{matrix}25x; &0\leq x\leq 40\\ 1000 + 32(x-40); & x > 40\end{matrix}\right.`