Question

a positive number is five times another number. if 21 is added to both the numbers ,then one of the new number become twice the other new number. what are the numbers?​

Answer 1

$\Large {\underline { \sf {Clarification :}}}$

Here, we are given that a positive number is five times another number and if 21 is added to both the numbers ,then one of the new number become twice the other new number. We have to find out the numbers.

We'll first assume two numbers as two variables, say x and y. After that, we'll form equations according to the question. By solving that equation we'll find the value of x and y.

$\Large {\underline { \sf {Explication \: of \: steps :}}}$

Given Information :

• A positive number is five times another number.

• If 21 is added to both the numbers ,then one of the new number become twice the other new number.

To calculate :

• The numbers.

Calculation :

Let a positive number be x and the another number be y.

According to the question,

» A positive number is five times another number.

$\longmapsto$ Positive Number = 5 × Another Number

$\longmapsto$ x = 5y

Let it be the equation (1) .

» If 21 is added to both the numbers ,then one of the new number become twice the other new number.

After adding 21 to both numbers :

$\longrightarrow$ First new number = x + 21

$\longrightarrow$ Another new number = y + 21

Equation :

$\longrightarrow$ First new number = 2 ( Another new number )

$\longrightarrow$ x + 21 = 2 (y+ 21)

$\longrightarrow \sf { x + 21 = 2 (y) + 2( 21)}$

$\longrightarrow \sf { x + 21 = 2y + 42}$

Now substitute the value of x from the equation (i).

$\longrightarrow \sf { 5y + 21 = 2y + 42}$

$\longrightarrow \sf { 5y - 2y= 42 - 21}$

$\longrightarrow \sf { 3y= 21 }$

$\longrightarrow \sf { y=\cancel{ \dfrac{ 21}{3} }}$

$\longrightarrow \: \boxed{\sf \red { y = 7 }}$

Now, let's find out the value of x. Substitute the value of y in the equation (1).

$\longrightarrow \sf { x = 5y}$

$\longrightarrow \sf { x = 5(7) }$

$\longrightarrow \: \boxed{\sf \red { x = 35 }}$

So, the numbers are 35 and 7.