money problem

Question

mensewar orderded short sleeve shirts for 23.00 each and long sleeve shirts for 28.50 each from Hugo boss. if the total amounted to 9,862.50 for 375 shirts how many of each were ordered

Answer 1

Short + Long = 375

23 x Short + 28.5 x Long = 9862.5

 

(Short + Long = 375)     multiply by -23 and add 
23 x Short + 28.5 x Long = 9862.5

 

(28.5 -23) x Long = 9862.50 -375 x 23

 

5.5 x Long = 1237.5

 

Long = 225, and

Short = 375 - 225 = 150

 

Answer 2

x = long sleeve

y = short sleeve

 

x+y = 375

23x + 28.50y = 9862.50

 

You can solve the equation by a number of different ways including finding the inverse of the equation, using substitution, using elimination, etc.

 

I personally would solve it by using elimination.  And to do this, you would multiply x+y=375 by -23 to get -23x-23y=-8625. 

 

 

Now you would put the equation above the second equation

 

-23x-23y=-8625

23x+28.50y=9862.50

 

You can cancel out the "x's" to get 5.50y=1237.50  You then divide 1237.50 by 5.50 to get 225.  So there are 225 short sleeve shirts.  Plug this value back into x + 225=375 and you will get 150 long sleeve shirts.