Question

One fourth of a number exceeds one fifth of its succeeding number by 3.Find the number.

Answer 1

Hi ,

We have to convert the given word problem into

algebraic equation.

Let the number = x

One fourth of the number = ( 1/4 ) × x = x / 4

Succeeding number of x = ( x + 1 )

One fifth of the above number = ( 1/5 ) × ( x + 1 )= ( x + 1 ) / 5


According to the problem ,

One fourhth of a number exceeds one fifth of its

succeeding number by 3.

x / 4 - ( x + 1 ) /5 = 3

LCM ( 4 , 5 ) = 4 × 5 = 20

[ 5x - 4 ( x + 1 ) ] / 20 = 3

5x - 4x - 4 = 3 × 20

x - 4 = 60

x = 60 + 4

x = 64

Therefore ,

Required number = x = 64

Verification:

x /4 - ( x + 1 ) /5 = 64 /4 - ( 64 + 1 ) / 5

= 16 - 13

= 3

I hope this helps you.

*****

Answer 2

Answer:

Step-by-step explanation:

Let the number = x

One fourth of the number = ( 1/4 ) × x = x / 4

Succeeding number of x = ( x + 1 )

One fifth of the above number = ( 1/5 ) × ( x + 1 )= ( x + 1 ) / 5

According to the problem ,

One fourhth of a number exceeds one fifth of its

succeeding number by 3.

x / 4 - ( x + 1 ) /5 = 3

LCM ( 4 , 5 ) = 4 × 5 = 20

[ 5x - 4 ( x + 1 ) ] / 20 = 3

5x - 4x - 4 = 3 × 20

x - 4 = 60

x = 60 + 4

x = 64

Therefore ,

Required number = x = 64