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 coming second in race. She scored 34 points but if the number of in which she came first and second were interchanged she would have scored 4 points less. Find x and y.

Answer 1

Step-by-step explanation:

5x+3y=34 _______(1)

3x+5y=30 _______(2)

equation(1)

5x= 34-3y

x= (34-3y)/5

now putting valueof x in equation (2)

3x+5y=30

3( (34-3y)/5 )+5y=30

(102-9y)/5 +5y=30

(102-9y+25y)/5=30

(102+16y) 5= 30

(102+16y)=30×5

16y=150-102

16y=48

y=48/16

y=3

now putting value of y in eq ^n (1)

x= (34-3y)/5

x=(34-3×3)/5

x=(34-9)/5

x=25/5

x=5

Amrita came first in x races= 5

Amrita came second in y races= 3