Question

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.

Answer 1

Here,

According to the conditions forming equations:

5x + 3y = 34     ...(1)

5y + 3x = 30

3x + 5y = 30     ...(2)

Now eliminate one variable, multiplying equation (1) by 5 and equation (2) by 3:

25x + 15y = 170     ...(3)

9x + 15y = 90     ...(4)

Subtracting equation (4) from equation (3):

(25x + 15y) − (9x + 15y) = 170 − 90

(25x − 9x) = 80

16x = 80

x = `80/16`

∴ x = 5

Substitute x = 5 into equation (1):

5(5) + 3y = 34

25 + 3y = 34

3y = 34 − 25

3y = 9

y = `9/3`

∴ y = 3