Question

one fourth of a number is 3 more than one fifth of its successor
find the number

Answer 1

x/4 = 3 + (x+1)/5
x/4 - (x+1)/5 = 3
(5x - 4x - 4)/20 = 3
x - 4 = 60
x = 64

Answer 2

The number is 64

Given :

One fourth of a number is 3 more than one fifth of its successor

To find :

The number

Solution :

Step 1 of 2 :

Form the equation to find the number

Let the required number is x

Then successor of the number = x + 1

By the given condition

$\displaystyle \sf \frac{x}{4} = \frac{1}{5} (x + 1) + 3$

Step 2 of 2 :

Find the number

$\displaystyle \sf \frac{x}{4} = \frac{1}{5} (x + 1) + 3$

$\displaystyle \sf{ \implies }\frac{x}{4} = \frac{x + 1}{5} + 3$

$\displaystyle \sf{ \implies }\frac{x}{4} = \frac{x}{5} + \frac{1}{5} + 3$

$\displaystyle \sf{ \implies }\frac{x}{4} - \frac{x}{5} = \frac{1}{5} + 3$

$\displaystyle \sf{ \implies }\frac{5x - 4x}{20} = \frac{15 + 1}{5}$

$\displaystyle \sf{ \implies }\frac{x}{20} = \frac{16}{5}$

$\displaystyle \sf{ \implies }x = \frac{16}{5} \times 20$

$\displaystyle \sf{ \implies }x = 64$

Hence the required number is 64

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