word problems

Question

The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 1/3 of it. Find the original fraction.

The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 

1

3

of it. Find the original fraction.The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 

1

3

of it. Find the original fraction.

Answer 1

let  denominator = x

 

numerator = x-5

 

so fraction =( x-5) /x

 

If the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by
1/3 ...this means the original fraction is equal to 2/3 times what it was originally. 

2*(x-5) / x+16 = 2/3*( (x-5)/x)

 

2*(x-5) / x+16 = 2* (x-5)/3x

 

 

2x -10 / x+16 = 2x-10 / 3x

 

3x(2x-10)=(x+16)(2x-10)

 

3x = x+16

 

2x= 16

 

x= 8

 

denominator = x =8

numerator = x-5 =8-5 =3

 

original fraction =3/8