Question

Translate the problem to a system of equations, then solve.

At a community college, the difference between a professor's salary and an associate professor's salary is $4,000. The sum of their salaries is $96,000. Find the salary of an associate professor at the college.
At a community college, the difference between a professor's salary and an associate professor's salary is $4,000. The sum of their salaries is $96,000. Find the salary of an associate professor at the college.

Answer 1

By setting up a system of equations with the given information, we can deduce that the salary of an associate professor at the community college is $46,000.

Step-by-step explanation:

To solve for the salary of an associate professor, we need to translate the problem into a system of equations and then solve it.

Let's define:

P = Salary of a professor

A = Salary of an associate professor

According to the problem, the difference between the salaries of a professor and an associate professor is $4,000 and the sum of their salaries is $96,000. This gives us two equations:

1. P - A = $4,000
2. P + A = $96,000

To find the values of P and A, we can use the method of elimination. Adding both equations, we eliminate A:

2P = $100,000

P = $50,000

Now that we have P, let's find A using the second equation:

P + A = $96,000

$50,000 + A = $96,000

A = $96,000 - $50,000

A = $46,000

The salary of an associate professor at the college is $46,000.