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The organisers of an essay competition decide that a winner in the competition get the price rupees 100.A participant who does not win gets a price of rupees 25.The total prize money distributed is rupees 3000.Find the number of winners if the total number of participants is 63.
Class 8 CBSE
Linear equations in one variable
Exercise 3.2 .
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Answers
Step-by-step explanation:
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.
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.