Chapter 6.1, Problem 34E

To determine

To calculate: The equivalent rate.

Answer to Problem 34E

The equivalent rate is $\$301$ per week.

Explanation of Solution

Given information:

The following equivalent fractions:

  $\frac{\$43}{\text{1 day}}=\frac{?\text{ dollars}}{1\text{ week}}$

Calculation:

To find an equivalent rate, convert from dollars per day to dollars per week. To do so, multiply the rate by a conversion factor. There are $7$ days in $1$ week, so $\frac{\text{7 days}}{\text{1 week}}=1$ .

  $\begin{array}{l}\frac{\$43}{\text{1 day}}\\ \Rightarrow \frac{\$43}{\text{1 day}}\times \frac{\text{7 days}}{\text{1 week}} \left[\text{Multiply rate by common conversion factor}\right]\\ \Rightarrow \frac{\$43}{\text{1 }\cancel{\text{day}}}\times \frac{\text{7 }\cancel{\text{days}}}{\text{1 week}} \left[\text{Divide out common factor and unit}\right]\\ \Rightarrow \frac{\text{\$301}}{1\text{ week}} \left[\text{Simplify}\right] \end{array}$

Therefore, the equivalent rate is $\$301$ per week.