Question

The sum of two integers is+20 and when we divide larger integer by smaller the result is-3
What are the 2integers

Answer 1

Step-by-step explanation:

let the first number be x and second number be (20-x)

x/20-x= -3

=> x= -3(20-x)

=> x= -60+3x

=> 3x-x=60

=> 2x= 60

=>. x= 30

The first number is 30 and

second number = (20-30)= -10

Answer 2

Answer:

-10 & 30

Step-by-step explanation:

As per the provided information in the given question, we have :

• The sum of two integers is 20.
• When the larger integer is divided by the smaller integer, the result is -3.

We are asked to find those two integer.

In order to tackle this problem, firstly we need to assum those two integers as two variable. Let us suppose two integers as x and y respectively. Let us assume that x is the larger integer and y is the smaller integer.

As per the given question, now we'll have to frame equations to find the value of x and y. According to the question,

$\longmapsto\rm { Number_{(Larger)} + Number_{(Smaller)} = 20 }$

Substitute the variables at the place of the larger number and the smaller number.

$\longmapsto\rm { x + y = 20 \; \bf {\dots (1)} }$

Now, also according to the question, when we divide larger integer by smaller the result is -3. Writing it in the form of an equation,

$\longmapsto\rm { \dfrac{Number_{(Larger)} }{ Number_{(Smaller)}} = -3 }$

Substitute the variables at the place of the larger number and the smaller number.

$\longmapsto\rm { \dfrac{x}{y} = -3 }$

Transpose y from L.H.S to R.H.S, its arithmetic operator will get changed.

$\longmapsto\rm { x = -3y \; \bf {\dots (2)} }$

Now, from this equation we got another equation which states that x is equivalent to the product of -3 and the smaller number.

In the equation (1), we have :

$\longmapsto\rm { x + y = 20 }$

Substitute the value of x from equation (2) to equation (1).

$\longmapsto\rm { -3y + y = 20 }$

Performing addition in L.H.S.

$\longmapsto\rm { -2y = 20 }$

Transposing -2 from L.H.S to R.H.S . Its arithmetic operator will get changed.

$\longmapsto\rm { y = \dfrac{20}{-2} }$

Dividing 20 by -2.

$\longmapsto\bf { y = -10 }$

We got the value of y that is -10. Now, substitute the value of y in the equation (1) to calculate the value of x.

$\longmapsto\rm { x + ( -10) = 20 }$

We can also write it as,

$\longmapsto\rm { x - 10= 20 }$

Transposing -10 from L.H.S to R.H.S. Its sign will get changed.

$\longmapsto\rm { x = 20 + 10}$

Performing addition in R.H.S.

$\longmapsto\bf { x = 30}$

We got the value of x that is 30.

∴ The two integers are -10 and 30.