Compare the two students' work to determine which student...

Compare the two students' work to determine which student did the work correctly. Explain what mistake the other student made. The same publicity company as in Exercise 37 has the following revenue equation: $$ R=0.95 b $$ where $R$ is the revenue in dollars from an order of $b$ custom-labeled bottles of water. Write an equation for the profit the publicity company will earn from an order of $b$ bottles $$ \begin{array}{|c|c|} \hline {\text { Rosemary }} & {\text { Will }} \\ P=\begin{array}{c} \text { Profit of each order in } \\ \text { dollars } \end{array} & \begin{array}{c} P=\text { Profit of each order } \\ \text { in dollars } \end{array} \\ \begin{array}{c} b=\text { number of bottles } \\ \text { ordered } \end{array} & \begin{array}{c} b=\text { number of bottles } \\ \text { ordered } \end{array} \\ P=0.95 b-(75+0.55 b) & P=0.95 b-75+0.55 b \\ P=0.95 b-75-0.55 b & P=-75+1.50 b \\ P=-75+0.40 b & \end{array} $$

Compare the two students' work to determine which student did the work correctly. Explain what mistake the other student made.
The same publicity company as in Exercise 37 has the following revenue equation:
$$
R=0.95 b
$$
where $R$ is the revenue in dollars from an order of $b$ custom-labeled bottles of water. Write an equation for the profit the publicity company will earn from an order of $b$ bottles
$$
\begin{array}{|c|c|}
\hline {\text { Rosemary }} & {\text { Will }} \\
P=\begin{array}{c}
\text { Profit of each order in } \\
\text { dollars }
\end{array} & \begin{array}{c}
P=\text { Profit of each order } \\
\text { in dollars }
\end{array} \\
\begin{array}{c}
b=\text { number of bottles } \\
\text { ordered }
\end{array} & \begin{array}{c}
b=\text { number of bottles } \\
\text { ordered }
\end{array} \\
P=0.95 b-(75+0.55 b) & P=0.95 b-75+0.55 b \\
P=0.95 b-75-0.55 b & P=-75+1.50 b \\
P=-75+0.40 b &
\end{array}
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Revenue and Profit Relationship

This concept involves understanding that profit is obtained by subtracting the total cost from the revenue. The revenue is the money received from sales, and the cost can have both fixed and variable components. Correctly establishing a profit equation requires identifying these two elements and combining them appropriately to reflect the actual earnings or losses.

Distributive Property in Algebra

A key step in forming the correct profit equation is applying the distributive property. When subtracting a sum (such as fixed cost plus variable cost multiplied by a quantity), it is necessary to distribute the negative sign to every term inside the parentheses. Failure to do so, as seen in one of the student’s work, can lead to errors in the simplified expression.

Simplifying Algebraic Expressions

After applying the distributive property, combining like terms is critical for a simplified and accurate expression. This process involves summing or subtracting coefficients for the same variable. An error in this arithmetic process, such as incorrect addition of coefficients, will result in an inappropriate representation of the profit function and ultimately an inaccurate solution.

Transcript

Please give Ace some feedback