Question

The organisers of an essay competition decide that a winner in the competition gets a prize of $100andaparticipantwhodoesnotwingetsaprizeof$25. The total prize money distributed is $3000. Find the number of winners, if the total number of participants is 63.

Answer 1

Given that there are 63 participants.

Let the number of winners be x

and number of non winners be (63-x)

Given that,

- winner get a prize of $100.-loosergetaprizeof$25
-Total prize amount is $3000.

therefore,
100x +25.(63-x)=3000
100x +25×63 - 25x=3000
75x =3000 - 25×63
=3000 -1575
=1425

75x=1425

there fore,

x=1425÷75
=19

So number of winners are 19.