5. Amrita came first in x races and second in y races. A score of 5 points is given for coming first and
3 points for the second place in a race. She scored 34 points but if the number of games in which
she came first and second were interchanged she would have scored 4 points less. Find x and y.
were for adults and others for students
15 each
Answers
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✤ Required Answer:
✒ GiveN:
- Amrita came first in x races.
- And, came second in y races.
- She gets 3 points for second places and 5 points for first places.
- And, scored 34 points.
- If the positions are interchanged, then she gets 4 points less.
✒ To FinD:
- Find x and y.....?
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✤ How to solve?
Taking the two variables, we can frame equations for given conditions and accordingly solving the equations to get the value of x and y. You can use Elimination or substitution method for solving. That's upon you....
⚘ So, let's solve the question....
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✤ Solution:
We have,
- x races with first position.
- y races with second position.
- 5 points for first position
- 3 points for second position.
From here, we can say that,
➝ Points obtained from 1st position = 5x
➝ Points obtained from 2nd position = 3y
Then, Total points obtained = 5x + 3y
Given ATQ,
➝ Total points = 34
➝ 5x + 3y = 34........(1)
Now, after interchanging,
- Races with 1st position = y
- Races with 2nd position = x
Then,
➝ Points obtained from 1st position = 5y
➝ Points obtained from 2nd position = 3x
Given ATQ,
➝ Total points = 34 - 4 = 30
➝ 3x + 5y = 30..........(2)
Adding eq.(1) and eq.(2),
➝ 5x + 3y + 3x + 5y = 64
➝ 8x + 8y = 64
➝ x + y = 8..........(3)
Subtracting eq.(2) from eq.(1),
➝ 5x + 3y -( 3x + 5y) = 4
➝ 5x + 3y - 3x - 5y = 4
➝ 2x - 2y = 4
➝ x - y = 2........(4)
From adding eq.(3) and eq.(4),
➝ x + y + x - y = 10
➝ 2x = 10
➝ x = 5
Putting value of x in eq.(3),
➝ 5 + y = 8
➝ y = 3
✒ Therefore,
- x races = 5 races (1st position)
- y races = 3 races (2nd position)
☸ Hence, solved !
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