Question

error analysis a company has two branches that are growing rapidly. branch 1 opened with 26 clients and they get 3 new clients each week. branch 2 opened with 39 clients and they get 12 new clients each week. a manager of the company wants to compare the number of clients each branch has, n, with respect to the number of weeks since the company opened, w. the manager incorrectly uses the system of equations below to compare the number of clients for each branch. n = 26w + 3 n = 39w + 12 what error might the manager have made? a. the manager multiplied by w instead of adding w. b. the manager switched the constant and coefficient of w in both equations. c. the manager combined the rates in one equation and the number of clients each branch started with in the other equation. d. the manager used the rate for branch 1 with the number of clients branch 2 started with and used the rate for branch 2 with the number of clients branch 1 started with.

Explanation:

Step1: Define correct equation structure

For each branch, the number of clients $n$ follows $n = \text{initial clients} + (\text{weekly new clients}) \times w$.

Step2: Write correct equations

Branch 1: $n = 26 + 3w$
Branch 2: $n = 39 + 12w$

Step3: Compare to manager's equations

Manager's equations: $n = 26w + 3$, $n = 39w + 12$. The initial client count is multiplied by $w$, and the weekly rate is the constant, which swaps the two values in both equations.

Answer:

B. The manager switched the constant and coefficient of w in both equations.