Question

Use two equations in two variables to solve the application.The salaries of the President and Vice President of a certain country total $572,400 a year. If the President makes $227,600 more than the Vice President, find each on their salaries (in dollars)

Answer 1

The President's salary is $400,000 and the Vice President's salary is $172,400, calculated using a system of equations based on the total and difference of their salaries.

Step-by-step explanation:

To solve for the salaries of the President and Vice President using a system of equations, we need to define two variables and set up two equations. Let's say that P represents the President's salary and V represents the Vice President's salary. From the given information, we can write the following equations:

1. P + V = $572,400
2. P = V + $227,600

We can solve these equations using substitution or elimination. Using substitution, we can take the second equation and substitute P from the first equation:

P + V = $572,400
V + $227,600 + V = $572,400
2V + $227,600 = $572,400
2V = $572,400 - $227,600
2V = $344,800
V = $172,400

Now we know the Vice President's salary; we can find the President's salary by using the second equation again:

P = V + $227,600
P = $172,400 + $227,600
P = $400,000

Hence, the President's salary is $400,000 and the Vice President's salary is $172,400.

Answer 2

Let the president's salary be x

Let the vice president's salary be y

The first statement of total salaries can be represented thus:

`x+y=572,400`

The president making more than the vice-president can be represented thus:

`x=227,600+y`

So we will substitute the x value above into the initial expression to get what their salaries will be:

`\begin{gathered} x+y=572400 \\ x=227600+y \\ 227600+y+y=572400 \\ 227600+2y=572400 \\ 2y=572400-227600 \\ 2y=344800 \\ y=(344800)/(2) \\ y=172400 \\ x=227600+y \\ x=227600+172400 \\ x=400000 \\ \text{The president's salary is \$400,000} \\ \text{The vice-president's salary is \$172,400} \end{gathered}`