Sure, let's break down the problem step by step to understand how to fill in the given table and answer the question effectively.
### Given Data:
- Total Earned at Hospital: \[tex]$3750
- Hourly Wage at Hospital: \$[/tex]16 per hour
- Total Earned at Mall: \[tex]$3750
### Step-by-Step Solution:
1. Calculate Hours Worked at the Hospital:
We know that the total amount earned at the hospital is \$[/tex]3750, and the hourly wage at the hospital is \[tex]$16 per hour. To find out the number of hours worked at the hospital, we can use the formula:
\[
\text{Hours Worked at Hospital} = \frac{\text{Total Earned at Hospital}}{\text{Hourly Wage at Hospital}}
\]
Substituting the values:
\[
\text{Hours Worked at Hospital} = \frac{3750}{16} = 234.375 \text{ hours}
\]
2. Assuming Same Number of Hours Worked at the Mall:
The problem assumes the worker worked the same number of hours at the mall as they did at the hospital. Therefore, the hours worked at the mall are also 234.375 hours.
3. Find Hourly Wage at the Mall:
We know the total earned at the mall is \$[/tex]3750 and the number of hours worked is 234.375 hours. To find the hourly wage at the mall, we can use the formula:
[tex]\[
\text{Hourly Wage at Mall} = \frac{\text{Total Earned at Mall}}{\text{Hours Worked at Mall}}
\][/tex]
Substituting the values:
[tex]\[
\text{Hourly Wage at Mall} = \frac{3750}{234.375} = 16 \text{ dollars per hour}
\][/tex]
### Filling in the Table:
[tex]\[
\begin{array}{|l|l|l|l|}
\hline
& \text{Rate (hourly wage)} & \text{Time (hours)} & \text{Total Earned} \\
\hline
\text{Hospital} & 16 \text{ dollars/hour} & 234.375 \text{ hours} & 3750 \text{ dollars} \\
\hline
\text{Mall} & 16 \text{ dollars/hour} & 234.375 \text{ hours} & 3750 \text{ dollars} \\
\hline
\end{array}
\][/tex]
Thus, the hourly wage at the mall is [tex]\(\boxed{16 \text{ dollars per hour}}\)[/tex].
