Question

The organizes of an debate competition decided that if a winner in the competition gets a prize of Rupees 100 and a participant who does not win gets a prize of Rupees 25. When he give total prize money distributed is Rs 3,000.
Find the number of winners, if the total number of participants is 63.

Answer 1

Given :-

In the competition,

• Awinner gets a prize of Rs 100.

• A participant who does not win gets a prize of Rs 25.

• Total prize money distributed = Rs 3,000.

• Total number of participants = 63

To Find :-

• Number of winners.

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problems

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

$\large\underline{\bold{Solution-}}$

• Let number of winners be 'x'.

According to statement,

• Total number of participants = 63

So,

• Total number of losers = 63 - x

Again,

According to statement,

• Winner get prize money of Rs 100

and

• Loser get prize money of Rs 25

So,

• Total prize money of 'x' winners = Rs 100x

and

• Total prize money of (63 - x) losers = 25(63 - x)

Now,

Given that

Total prize money distributed = Rs 3000

$\sf \: \therefore \: 100x + 25(63 - x) = 3000$

$\sf \: 100x + 1575 - 25x = 3000$

$\sf \: 100x - 25x = 3000 - 1575$

$\sf \: 75x = 1425$

$\bf \: \therefore \: x \: = \: 19$

Hence,

• Number of winners = 19.

Answer 2

Answer:

Let x be the number of winners.

Then the number of participants who do not win is given as (63 – x)

The prize money given to x winners = Rs ( 100x)

The prize money given to (63 – x) participants is = Rs 25(63 – x)

According to the given data, the total prize money distributed = Rs 3000

Therefore, 100x + 25(63 – x) = 3000

4x + (63 – x) = 120

3x + 63 = 120

x = 19

Therefore, the number of winners is 19.