Question

The organizer 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 of$25 . The total price money distributed is $3000. Find the number of participants is 63

Answer 1

Step-by-step explanation:

Answer:-

Given:-

• the total price money distributed is $3000.
• the winner in the competition gets a prize of $100.
• the participants who doesn't win gets a prize of $25.
• the number of participants is 63.

To find:-

• the number of winners.

Solution:-

$Let \: \: the \: \: numbers \: \: of \: \: winner \: \: be \: \: x.$

$Then, \: the \: number \: of \: participants \: who \: didn't \: win \: = \: 63 \: - \: x$

$Total \: money \: given \: t o \: the \: winner \: = \: x \: × \: 100 \: = \: 100x$

$Total \: money \: given \: to \: participant \\ who \: didn't win \: = \: 25 \: × \: (63 \: - \: x)$

$According \: \: to \: \: the \: \: question,$

$100x \: + \: 25×(63 \: - \: x) \: = \: 3,000$

$⇒ \: 100x \: + \: 1575 \: - \: 25x \: = \: 3,000$

$⇒ \: 75x \: = \: 3,000 \: - \: 1575$

$⇒ \: 75x \: = \: 1425$

$⇒ \: x \: = \: \frac{1425}{75}$

$⇒ \: x \: = \: 19$

$∴ \: Hence,\:the \: numbers \: of \: winners \: are \: 19.$

Answer 2

Given :-

• Prize amount for winners = $100
• Prize amount for participants who didn't win = $ 25
• Total number of participants = 63
• Total prize money distributed = $3000

To Find :-

• The number of winners

Solution :-

$\sf \: \sf Let \: the \: number \: of \: winners \: be \: x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\therefore \: Number \: of \: participants \: who \: didn't \: win = 63 - x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf Total \: money \: given \: to \: the \: winners = 100 \times x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf Money \: given \: to \: the \: participants \: who \: didn't \: win = 25 \times (63 - x)$

$\sf \: Now \: , \: According \: to \: the \: question \: \: \: \: \: \: \: \: \: \\ \sf \longrightarrow \red{100x + 25 \times 63 - x = 3000} \: \: \: \: \: \: \: \: \\ \: \sf \longrightarrow \gray {75x = 3000 - 1575} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \\ \sf \longrightarrow \green {x = \frac{1425}{75} = \frac{ \cancel{1425}}{ \cancel{75}} = 19} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\therefore \pink {Number \: of \: winners \: = x = 19} \: \: \: \: \: \: \: \: \: \: \:$

$• \sf \: number \: of \: winners \: = x = 19 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ • \sf\: number \: of \: participants \: who \: did \: not \: win = \: \\ \sf \longrightarrow 63 - x = 63 - 19 = 44 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$