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.

a) Governor of state A: $171,575, Governor of state B: $117,830

b) Governor of state A: $171,575, Governor of state B: $225,230

c) Governor of state A: $235,290, Governor of state B: $181,545

d) Governor of state A: $289,405, Governor of state B: $235,660

Answer 1

x + x + $53,745 = $289,405

2x = $235,660

x = $117,830

State A: $117,830 + $53,745 = $171,575

State B: $117,830

The correct answer is A.

Answer 2

The salaries for the governors of state A and state B are $171,575 and $117,830 respectively, calculated by solving a system of linear equations.

Step-by-step explanation:

The student is asking to find the salaries of the governors from state A and state B given that the governor of state A earns $53,745 more than the governor of state B and the total of their salaries is $289,405.

Let's denote State A's governor's salary as A and State B's governor's salary as B. The problem gives us two equations to work with:

1. A = B + $53,745
2. A + B = $289,405

To solve this, we substitute the first equation into the second:

• B + $53,745 + B = $289,405
• 2B + $53,745 = $289,405
• 2B = $289,405 - $53,745
• 2B = $235,660
• B = $117,830

Now we can find A using the first equation:

• A = $117,830 + $53,745
• A = $171,575

Therefore, the correct salaries are:

• Governor of state A: $171,575
• Governor of state B: $117,830