Question

The governor of state A eams $49,350 more than the govemor of state B. If the total of their salaries is $296,370, find the salaries of each.

Answer 1

Governor of state A makes $172,860.

Governor of state B makes $123,510.

Explanation:

Let the governor of state A be denoted by the variable x.

Let the governor of state B be denoted by the variable y.

Set the system of equations:

x = 49350 + y

x + y = 296370

First, plug in 49350 + y for x in the second equation, and then simplify:

x + y = 296370

(49350 + y) + y = 296370

Combine like terms:

49350 + (y + y) = 296370

49350 + 2y = 296370

Isolate the variable, y. Do the opposite of PEMDAS. Note the equal sign, what you do to one side, you do to the other.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

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First, subtract 49350 from both sides of the equation:

2y + 49350 (-49350) = 296370 (-49350)

2y = 296370 - 49350

2y = 247020

Next, divide 2 from both sides of the equation:

(2y)/2 = (247020)/2

y = 247020/2

y = 123510

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Plug in 123510 for y in one of the equations given in the system of equation:

x = 49350 + y

x = 49350 + 123510

x = 172860

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Check. Plug in 123510 for y, and 172860 for x in the given equation:

x + y = 296370

(172860) + (123510) = 296370 (True).

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