# Ex 2.2, 16 - Chapter 2 Class 8 Linear Equations in One Variable

Last updated at June 21, 2018 by Teachoo

Last updated at June 21, 2018 by Teachoo

Ex 2.2, 16 The organisers of an essay competition decide that a winner in the competition gets a prize of Rs 100 & a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3,000. Find the number of winners, if the total number of participants is 63.Given, Prize given to the Winner = Rs 100 Prize given to the participants who did not win = Rs 25 Total Prize money = Rs 3,000 Total number of participants = 63 Let the numbers of winners = 𝑥 Then, Total no. of participants = Number of winners + Number of participants who did not win 63 = 𝑥 + Number of participants who did not win 63 − 𝑥 = Number of participants who did not win Number of participants who did not win = 63 − 𝑥 Total amount given to the winners = Number of winners × Amount given to 1 winner = 𝑥 × 100 = 100𝑥 Total amount given to the participants who did not win = Number of participants who did not win × Amount given to 1 participant = (63 − 𝑥) × 25 = 63 × 25 − 𝑥 × 25 = 1575 − 25𝑥 Total prize money = Total amount given to winners + Total amount given to participants who did not win 3000 = 100𝑥 + 1575 − 25𝑥 100𝑥 + 1575 − 25𝑥 = 3000 75𝑥 + 1575 = 3000 75𝑥 = 3000 − 1575 75𝑥 = 1425 𝑥 = 1425/75 𝑥 = 19 Therefore, the number of winners = 19