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.
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)
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)
(3 3/4 B + $3250 = 2B + $6400)
1 3/4 B + $3250 = $6400
1 3/4 B = $3150
B = $1800 (Enter this into A = 3/4 B + $650)
A = 3/4 ($1800) + $650
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
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
Then plug A back into the first equation:
5(2000)= 2B + 6400
10000= 2B + 6400
Then you would check to make sure the answers made sense in the problem.