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. write a system of equations that the manager can use to compare the number of clients for each branch. what error might the manager have made? n = 26w + 3 n = 39w + 12 a. n = 26 + 3w n = 39 + 12w b. n = 26 + 39 n = 3w + 12w c. n = 26w + 12 n = 39w + 3 d. n = 26 + 12 + w n = 39 + 3 + w

Explanation:

Step1: Define Branch 1's client count

The initial clients are 26, plus 3 new per week.
$n = 26 + 3w$

Step2: Define Branch 2's client count

The initial clients are 39, plus 12 new per week.
$n = 39 + 12w$

Step3: Match to error options

The manager mixed up growth rates with initial counts, swapping coefficients of $w$ and constants. This matches option A.

Answer:

A. $n = 26 + 3w$
$n = 39 + 12w$