Answer:
Salary of state A's governor = $170,465
Salary of state B's governor = $118,145
Explanation:
We will need a system of equations to find the salaries of each governor.
Let A represent the salary of state A's governor and B represent the salary of state B's governor.
Step 1: Write an equation showing that state A's governor's salary is $52320 higher than state B's governor:
Since the governor of state A earns $52320 more than the governor of state B, we can model this with the equation:
A = B + 52320
Step 2: Write an equations showing that the sum of the two governor's salaries is $288610:
The equation modeling the sum of the governor's salaries is given by:
A + B = 288610
Step 3: Plug in A = B + 52320 for A in A + B = 288610 to solve for B:
Now, we can plug in A = B + 52320 for A in A + B = 288610 to solve for B:
B + 52320 + B = 288610
Combining like terms gives us:
2B + 52320 = 288610
Subtracting 52320 from both sides gives us:
2B = 236290
Dividing both sides by 2 gives us:
B = 118145
Step 4: Find A, the salary of state A's governor:
We can plug in 118145 for B in A + B = 288610 to find A, the salary of state A's governor:
A + 118145 = 288610
Subtracting 118145 from both sides gives us:
A = 170465
Thus, the salary of state A's governor is $170,465 and the salary of state B's governor is $118,145.