two salaries of 2 people

Question

The government of state A earns 50,815 more than the government of state b. If the total of their salaries is 308,545, find the salaries of each.

Answer 1

Hi, Austin,

 

This is a word problem in which you can set up a system of equations. Let x = the salary for state A and y = the salary for state B. It states that the total of their salaries is 308,545, so this simply means you have to add the two salaries, so you can write: x + y = 308,545. Also, the problem mentions that state A earns 50,815 more than that of state B, so you can say state A = state B + 50,815, or, in terms of variables, x = y + 50,815. So your two equations are:

 

x+ y = 308,545  and    x = y + 50,815

 

You can use a substitution method by plugging what x is from the right equation into the left equation. 

 

x + y  = 308,545  becomes  (y+50,815) + y = 308,545 

 

Combining like terms gives you

 

2y + 50,815= 308,545

 

Subtracting 50,815 on both sides (to solve for y) gives you:

 

2y + 50,815-50,815= 308,545-50,815

 

2y = 257,730

 

Now, you must divide both sides by 2 in order to solve for y:

 

2y/2= 257,730/2

 

y = $128,865; so this is the salary of the government of state B

 

Now we can plug this value into x = y + 50,815 to get x:

 

x = y + 50,815 = 128,865+50,815 = $179,680; this is the salary of the government of state A

 

That is all there is to it :)

 

Emmanuel

Answer 2

Let x = salary state b

 

x + 50,815 = salary state a

 

x + x + 50,815 = 308,545

 

2x + 50,815 = 308,545

 

2x = 257,730

x = 128,865  salary state b

 

179,680 salary state a

 

I'd gladly take a job in either state!!!!!!