Question

helene considers two jobs. one pays $51,000/yr with an anticipated yearly raise of $4150. a second job pays $53,000/yr with yearly raises averaging $3900.
part 1 of 3
(a) write a model representing the salary ( s_1 ) (in $) for the first job in ( x ) years.
the model representing the salary (in $) for the first job in ( x ) years is ( s_1 = square ).
part 2 of 3
(b) write a model representing the salary ( s_2 ) (in $) for the second job in ( x ) years.
the model representing the salary (in $) for the second job in ( x ) years is ( s_2 = square ).
part 3 of 3
(c) in how many years will the salary from the first job equal the salary from the second? round to the nearest year, if necessary.
the salary for the first job will equal the salary from the second job in ( square ) years.

Explanation:

Part 1 of 3 (a)

Step1: Identify initial salary and raise

Initial salary for first job: $51000, yearly raise: $4150.

Step2: Form linear model

Salary \( S_1 \) after \( x \) years is initial salary + (raise per year * years). So \( S_1 = 51000 + 4150x \).

Step1: Identify initial salary and raise

Initial salary for second job: $53000, yearly raise: $3900.

Step2: Form linear model

Salary \( S_2 \) after \( x \) years is initial salary + (raise per year * years). So \( S_2 = 53000 + 3900x \).

Step1: Set \( S_1 = S_2 \)

Set \( 51000 + 4150x = 53000 + 3900x \).

Step2: Solve for \( x \)

Subtract \( 3900x \) and 51000 from both sides: \( 4150x - 3900x = 53000 - 51000 \).
Simplify: \( 250x = 2000 \).
Divide by 250: \( x = \frac{2000}{250} = 8 \).

Answer:

\( 51000 + 4150x \)

Part 2 of 3 (b)