Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Craig is paid time-and-a-half for any additional hours over that he works.

Time	Pay Rate
Up to hours	\($\mathbf{12}\mathbf{.80}\mathbf{/}\mathbf{\text{hr}}$
Additional hours worked over $\mathbf{40}$	\)$\mathbf{19}\mathbf{.20}\mathbf{/}\mathbf{\text{hr}}$

If Craig’s goal is to earn at least $$\mathbf{600}$next week, what is the minimum number of hours he needs to work?

F $\mathbf{43}\mathit{h}\mathit{o}\mathit{u}\mathit{r}\mathit{s}$

G $\mathbf{44}\mathit{h}\mathit{o}\mathit{u}\mathit{r}\mathit{s}$

H $\mathbf{45}\mathit{h}\mathit{o}\mathit{u}\mathit{r}\mathit{s}$

J $\mathbf{46}\mathit{h}\mathit{o}\mathit{u}\mathit{r}\mathit{s}$

Short answer

The minimum number of hours he needs to work is $\mathbf{45}\mathit{h}\mathit{o}\mathit{u}\mathit{r}\mathit{s}$. Therefore, the option$\mathit{H}$ is correct.

Step-by-step solution

Step 1. Given

Time	Pay Rate
Up to hours	$\$12.80/hr$
Additional hours worked over$40$	$\$19.20/hr$

Step 2. Write the inequality for the given situation.

Let $x$be the number of additional hours that he worked over .

It is given that the pay rate for working up to $40hours$is $\$12.80/\text{hr}$and pay rate for working over 40 hours is $\$19.20/\text{hr}$and he earns at least $\$600$next week.

Therefore, the inequality for the given situation is:

$\begin{array}{c}12.80\times 40+19.20\times x\ge 600\\ 512+19.2x\ge 600\end{array}$

The inequality for the given situation is $512+19.2x\ge 600$.

Step 3. Determine the minimum number of hours he needs to work.

Solve the inequality $512+19.2x\ge 600$.

$\begin{array}{c}512+19.2x\ge 600\\ 512-512+19.2x\ge 600-512\\ 19.2x\ge 88\\ x\ge \frac{88}{19.2}\\ x\ge 4.5833\end{array}$

Therefore, the minimum value of $x$an integer is 5.

Therefore, the minimum number of additional hours that he worked over 40 is 5.

Therefore,the minimum number of hours he needs to work is given by:

$40+5=45$

The minimum number of hours he needs to work is $45hours$. Therefore, the option$H$ is correct.