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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.

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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

Thank you very much Shannon!! You made that very clear and helped me understand how to set the up equations! :)

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

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