Word problem on equation and inequalities

Question

the top four medal winners in all sports during the 2012 summer olympics were michael phelps, Missy Franklin, Allison Schmit, and Ryan Lochte. The total number of medals won by these athletes was 21. Phelps won one more medal than Franklin. Schmitt won the same number of medals as Franklin. Lochte won 5 less than twice as many medals as franklin. How many medals did each athlete win?

Answer 1

Let x = number of medals won by Phelps

       y = number of medals won by Franklin

       z = number of medals won by Schmit

       w = number of medals won by Lochte

 

x + y + z + w = 21

x = y + 1

y = z

w = 2y - 5

 

Since y = z, the system can be reduced to:

 

x + 2y + w = 21

x = y + 1

w = 2y - 5

 

Replace x by  y + 1 in the first equation:

 

y + 1 + 2y + w = 21

 

So, 3y + 1 + w = 21

 

We have:  w = 20 - 3y

 

But, w = 2y - 5

 

So, 20 - 3y = 2y - 5

             -5y = -25

                 y = 5           x = y + 1 = 6

                                    w = 2y - 5 = 5

                                     z = y = 5

                                    

 

ANSWER:  x = 6, y = z = w = 5