I'm not sure how to set this problem up and would like to see how it's done. Thanks!

## If 5 times A's salary exceeds twice B's by $6400, and 4 times A's salary exceeds 3 times B's by $2600, find the salary of each man and show work.

# 2 Answers

Sometimes it is easiest to write the words of the problem using math symbols to find the equation you are being asked to solve:

5A = 2B + $6400 and **4A = 3B + $2600**

You need to use one equation and get one variable alone. I chose the one in **
bold**.

4A = 3B + $2600 (divide both sides by 4)

4 4

A = 3/4 B + $650 (Now you have solved for A. Use this in the other equation for A.)

5(3/4 B + $650) = 2B + $6400 (You must multiply A by 5 before you continue.)

15/4 B + $3250 = 2B + $6400 ( Solve for B by moving all B's to one side. Also, 15/4 = 3 3/4)

-2B -2B

(3 3/4 B + $3250 = 2B + $6400)

-2B -2B

1 3/4 B + $3250 = $6400

-$3250 -$3250

1 3/4 B = $3150

B = $1800 (Enter this into A = 3/4 B + $650)

A = 3/4 ($1800) + $650

A= $2000

Mitchell,

We need to translate the words in this problem into some form of equation:

If 5 times A's salary= 5*A or 5A

exceeds twice B's by 6400= is more than 2B by 6400= 2B+6400

So, 5A= 2B+6400

Then, we set up another equation:

4 times A's salary= 4A

exceeds 3 times B's salary by 2600= 3B+2600

So, 4A=3B+2600

Now we have a system of equations.

5A= 2B + 6400

4A= 3B + 2600

If we multiply the first equation by -3 and the second by 2 we get:

-15A= -6B - 19200

8A= 6B + 5200

So the B's will cancel.

Then we add them together:

-7A = -14000

A= 2000

Then plug A back into the first equation:

5(2000)= 2B + 6400

10000= 2B + 6400

2B=3600

B= 1800

Then you would check to make sure the answers made sense in the problem.

Good luck!

## Comments

You're very welcome Courtnee! I'm glad that you understand it now :D

Comment