Question

The difference between two positive integers is 51 the quotient when one integers is divided by the other is 4 find the two integers

Answer 1

Given :-

The difference between two positive integers is 51.

The quotient when one integers is divided by the other is 4.

To Find :-

The first integer.

The second integer.

Analysis :-

Consider the integers as variables.

According to the question, make an equation and substitute the values accordingly.

Solution :-

Let the two integers be 'x' and 'y'.

At first,

$\sf x - y = 51$

$\sf x=51+y \qquad ....(1)$

Then,

$\sf \dfrac{x}{y} =4 \qquad ....(2)$

Putting the values in equation (1) and (2),

$\sf \dfrac{x}{y} =4$

$\sf \dfrac{51+y}{y} =4$

$\sf 51+y = 4y$

$\sf 4y-y = 51$

$\sf 3y = 51$

Finding the value of y,

$\sf y=\dfrac{51}{3}$

$\sf y=17$

Substituting the value of y,

$\sf x = 51+y$

$\sf x = 51+17$

$\sf x = 68$

Therefore,

x = 68

y = 17

Hence, the two integers are 68 and 17.