Question

2.4.3 quiz: linear equa
question 4 of 10
a webmaster makes $24 an hour for the first 38 hours she works during a week and $31 an hour for each hour worked over 38 hours. which piecewise equation models her total weekly pay y in dollars as it relates to the number of hours x that she has worked during the week?
\\(\boldsymbol{\text{ a. } y=\

$$\begin{cases}24x & 0 \\leq x \\leq 38 \\\\ 31(x - 38) & x > 38 \\end{cases}$$

}\\)
\\(\boldsymbol{\text{ b. } y=\

$$\begin{cases}24x & 0 \\leq x \\leq 38 \\\\ 31x + 912 & x > 38 \\end{cases}$$

}\\)
\\(\boldsymbol{\text{ c. } y=\

$$\begin{cases}24x & 0 \\leq x \\leq 38 \\\\ 31x & x > 38 \\end{cases}$$

}\\)
\\(\boldsymbol{\text{ d. } y=\

$$\begin{cases}24x & 0 \\leq x \\leq 38 \\\\ 31(x - 38) + 912 & x > 38 \\end{cases}$$

}\\)
submit

Explanation:

Step1: Analyze pay for \(0\leq x\leq 38\)

For the first 38 hours, the pay rate is $24 per hour. So the pay \(y = 24x\) when \(0\leq x\leq 38\).

Step2: Analyze pay for \(x > 38\)

First, calculate the pay for 38 hours: \(24\times38 = 912\) dollars. For hours over 38 (i.e., \(x-38\) hours), the rate is $31 per hour. So the total pay is the pay for 38 hours plus the pay for the extra hours: \(y=31(x - 38)+912\) when \(x > 38\).

Step3: Match with options

Option D has the correct piecewise function: \(y=

$$\begin{cases}24x & 0\leq x\leq 38\\31(x - 38)+912 & x>38\end{cases}$$

\).

Answer:

D. $y=

$$\begin{cases}24x & 0\leq x\leq 38\\31(x - 38)+912 & x>38\end{cases}$$

$