Question

) The organisers of a dance competition decided that the winners of the competition would
get a prize money of R5000 each and the participants who did not win would get R7
each. The total prize money distributed was 1,60,000.
(i) Find the number of winners, if the total number of participants was 100.
(i) Out of the total number of winners, the number of girls was three times the number of
boys. Find the number of boys and the number of girls who won​

Answer 1

Answer:

Let x be the number of the winners. So, the number of participants who does not win (63−x).

Prize money given to x winners = Rs. (100×x)= Rs. 100x

and prize money given to (63−x) participants = Rs. 25(63−x)

Given, total prize money distributed = Rs. 3000

∴100x+25(63−x)=3000

⇒4x+(63−x)=120 ...[On dividing both sides by 25]

⇒3x+63=120

⇒3x=120−63 ...[Transposing 63 to RHS]

⇒3x−57⇒x=

3

57

=19

∴ The number of winners is 19