SOLUTION: The organisers of an essay competition decide that a winner in the competition gets a prize of $100 and a participant who does not win gets a prize a $25. The total prize money dis

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The organisers of an essay competition decide that a winner in the competition gets a prize of $100 and a participant who does not win gets a prize a $25. The total prize money dis      Log On


   

Question 1040470: The organisers of an essay competition decide that a winner in the competition gets a prize of $100 and a participant who does not win gets a prize a $25. The total prize money distributed is $3000. Find the number of winners , if the total number of participants is 63.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the number of winners
+63+-+x+ = the number of non-winners
-----------------------------------
given:
+100x+%2B+25%2A%28+63+-+x+%29+=+3000+
+100x+%2B+1575+-+25x+=+3000+
+75x+=+3000+-+1575+
+75x+=+1425+
+x+=+19+
and
+63+-+x+=+63+-+19+
+63+-+x+=+44+
------------------
There are 19 winners
----------------------
check:
+100x+%2B+25%2A%28+63+-+x+%29+=+3000+
+100%2A19+%2B+25%2A44+=+3000+
+1900+%2B+1100+=+3000+
+3000+=+3000+
OK