Question

a fraction becomes 1/3, if 2 is added to both numerator and denominator if if 3 is added to both numerator and denominator, it becomes 2/5 assuming the fraction to be [x/y], formulate two equations in two variables to represent the above problem​

Answer 1

Answer:

let numerator be x and denominator be y.

according to question,

x + 2 / y + 2 = 1/ 3

= 3 ( x + 2 ) = y + 2

3x + 6 = y + 2

3x - y = 2 - 6

3x - y = - 4 - ( 1 )

second case :

x + 3 / y + 3 = 2 / 5

5 ( x + 3 ) = 2 ( y + 3 )

5x + 15 = 2y + 6

5x - 2y = 6 - 15

5x - 2y = - 9 - ( 2 )

using elimination method

multiply ( 1 ) by 5 and ( 2 ) by 3

= 5 ( 3x - y = - 4 )

15x - 5y = - 20 - ( 3 )

= 3 ( 5x - 2y = - 9 )

15x - 6y = - 27 - ( 4 )

subtract ( 3 ) and ( 4)

15x - 5y = - 20

15x - 6y = - 27

- + +

_______________

y = 7

_______________

put value of y in ( 1 )

3x - y = - 4

3x - 7 = - 4

3x = - 4 + 7

3x = 3

x = 3 / 3

x = 1

so, x = 1 and y = 7

I hope you understand.

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