Question

The denominator of a rational number is greater than its numerator by 7.If 3 is subtracted from the numerator and 2 is added to its denominator .The new number becomes 1/5 find the rational numbers.

Answer 1

HERE IS YOUR ANSWER
Let denominator be x & numerator be y
From 1st condition,
x-7=y.
x-y=7. ......................(1)
From 2nd condition,
y-3÷x+2=1÷5.
5y-15=x+2.
x-5y=17. ....................(2)
By sustracting eqn 1 from eqn 2 we get,
-6y=24
y=-4
By putting value y=-4 in eqn 1 we get,
x-(-4)=7
x+4=7
x=7-4
x=3
Hence,(x,y)=(3,-4) is the solution.
I HOPE THIS HELP YOU!!!