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# 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.

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

### 2 Answers by Expert Tutors

Gretchen S. | Credentialed Teacher and Homeschool MomCredentialed Teacher and Homeschool Mom
2

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

Shannon M. | Biology Major Specializing in Science and MathBiology Major Specializing in Science an...
4.9 4.9 (83 lesson ratings) (83)
1

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.

-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!