Questions: If Amber is paid 8 per hour for typing, the table shows how much she earns. Hours (h) 1 2 3 4 5 Wages (w) 8 16 24 32 40 a. How much would Amber make for a 25-hr work week? b. What is the constant of proportionality?

If Amber is paid 8 per hour for typing, the table shows how much she earns.

Hours (h) 1 2 3 4 5
Wages (w) 8 16 24 32 40

a. How much would Amber make for a 25-hr work week?
b. What is the constant of proportionality?

Transcript text: If Amber is paid $\$ 8$ per hour for typing, the table shows how much she earns. \begin{tabular}{|c|c|c|c|c|c|} \hline Hours ( $\mathbf{h})$ & 1 & 2 & 3 & 4 & 5 \\ \hline Wages $(\mathbf{w})$ & $\$ 8$ & $\$ 16$ & $\$ 24$ & $\$ 32$ & $\$ 40$ \\ \hline \end{tabular} a. How much would Amber make for a 25 -hr work week? b. What is the constant of proportionality?

Solution

Solution Steps

Solution Approach

a. To find out how much Amber would make for a 25-hour work week, we need to multiply the number of hours (25) by her hourly wage ($8).

b. The constant of proportionality in this context is the hourly wage, which is the amount Amber earns per hour. This can be determined by dividing the wages by the number of hours for any entry in the table.

Step 1: Calculate Earnings for a 25-Hour Work Week

To find Amber's earnings for a 25-hour work week, we use the formula: \[ \text{Earnings} = \text{Hourly Wage} \times \text{Hours Worked} \] Substituting the values: \[ \text{Earnings} = 8 \, \text{USD/hour} \times 25 \, \text{hours} = 200 \, \text{USD} \]

Step 2: Determine the Constant of Proportionality

The constant of proportionality is defined as the amount earned per hour, which can be calculated as: \[ \text{Constant of Proportionality} = \frac{\text{Wages}}{\text{Hours}} \] Using the first entry in the table: \[ \text{Constant of Proportionality} = \frac{8 \, \text{USD}}{1 \, \text{hour}} = 8 \, \text{USD/hour} \]