The governor of state A earns $49,425 more than the governor of state B. If the total of their salaries is $291,025, find the salaries of each.

Question

I dont get this question at all and need help trying to find both of the salaries for governor A and state B. If state A earns $49,425 more than governor B then how much would they earn together

Answer 1

Hello, Alexus

I admire the fact that you are doing math on a Saturday night. Great.

 

Well, let's start by setting up the problem.

 

Let a be the salary of the governor of state A

Let b be the salary of the governor of state B

 

Now, we know that more than means addition. So, the problem states that the governor of state b earns 49,425 more than the governor of state a.  Translating this into algebra we have

b= a+ 49,425  or b-49,425  = a , both of this equations convey the same idea that the governor of b makes more money than the governor of a.  

 

Next, the problem states that the total ( the sum) of their salaries is equal to 291,025. Translating into algebra

 

a+b= 291,025 , note that this equation has two different variables. 

 

What we need to do is to substitute for a, so we can solve this equation in terms of b.  So, whenever you see an a you will plug in the value of a in terms of b. 

 

So, a+b= 291, 025 becomes b-49,425 + b = 291,025. Combining like terms, we have 2b -49, 425= 291, 025

2b= 340, 450     We get this by adding 49,425 to both sides

b= 170,225.  

 

Finally,the governor of A earns 170, 225, and the governor of A earns 120, 800. 

 

That should be the answer.

 

D.Y. Taylor

 

 

 

 

Answer 2

Ok, let’s build the problem using the numbers given.
 

The problem would look like this:
Gov B + Gov A = 291,025

Gov B = X
As Gov A makes 49,425 more than Gov B, it is represented as X + 49,425

So our formula is:
X + X + 49,425 = 291,025

We can simplify that to:
2X + 49,425 = 291,025

Now to solve it, let’s put as many numbers on the same side of the = as possible (keeping in mind we have to change the signs when crossing the = sign.)

2X = 291,025 – 49,425 (see how + became - when crossing the =)

Simplified, it looks like:
2X = 241,600

Ok, to move the 2 of 2X over, I change again (multiplication to division), so it looks like:
X = 241,600/2 (or 241,600 divided by 2)

Solving for X
X = 120,800

We can check our math by plugging the number back into the original formula instead of using X
120,800 + 120,800 + 49,425 = 291,025