Question

The governor of state A earns $53,745 more than the governor of state B. If the total of their salaries is $289,405, find the salaries of each.

Answer 1

The salary of the governor of state A is $171,575 and the salary of the governor of state B is $117,830.

Explanation:

If the governor of state A's salary is "x" and the governor of state B's salary is "y", then:

`x = y + 53,745`

If the total of their salaries is $289,405, then the sum of x and y should be equal to that number.

`x + y = 289,405\\`

Applying the first expression on the second allows us to solve for y as shown below.

`y + 53745 + y = 289405\\2y = 289405 - 53745\\2y = 235660\\y = 117830`

Using this data on the first expression allows us to solve for the first governo's salary.

`x = 117830 + 53745 = 171575`

The salary of the governor of state A is $171,575 and the salary of the governor of state B is $117,830.