Question

the sum of two numbers is 21 and their difference is 3 what are the two numbers ?

Answer 1

Answer:

Required Answer:-

Let the numbers are x and y

${\qquad}{:}\longrightarrow\sf x+y=21\dots\dots(1)$

${\qquad}{:}\longrightarrow\sf x-y=3\dots\dots(2)$

• Add both equations

${\qquad}{:}\longrightarrow\sf x+\bcancel {y}+x-\bcancel {y}=21+3$

${\qquad}{:}\longrightarrow\sf 2x=24$

${\qquad}{:}\longrightarrow\sf x={\dfrac{24}{2}}$

${\qquad}{:}\longrightarrow\sf x=12$

• Substitute the value in eq (1)

${\qquad}{:}\longrightarrow\sf x+y=21$

${\qquad}{:}\longrightarrow\sf 12+y=21$

${\qquad}{:}\longrightarrow\sf y=21-12$

${\qquad}{:}\longrightarrow\sf y=9$

$\therefore$ The numbers are 12 and 9.

Confused!! Let's verify:-

Case-1:-

${\qquad}{:}\longrightarrow\sf x+y=21$

${\qquad}{:}\longrightarrow\sf 12+9=21$

${\qquad}{:}\longrightarrow\sf 21=21 {}_{(proved)}$

Case-2:-

${\qquad}{:}\longrightarrow\sf x-y=3$

${\qquad}{:}\longrightarrow\sf 12-9=3$

${\qquad}{:}\longrightarrow\sf 3=3 {} _{(proved)}$

Answer 2

Answer :

The required numbers are 12 and 9

Step-by-step explanation :

Let the numbers be x and y

Given that, x + y = 21 and x - y = 3

Let's find the x first,

x + y = 21

Then, y = 21 - x

⟹ x - ( 21 - x ) = 3

⟹ x - 21 + x = 3

⟹ 2x = 21 + 3

⟹ 2x = 24

⟹ x = 24/2

⟹ x = 12

Now, Let's find y ,

As, we got x = 12, Then,

⟹ 12 + y = 21

⟹ y = 21 - 12

⟹ y = 9

Therefore, the numbers are 12 and 9

Now, Verification

Given that, x + y = 21 and x - y = 3

By putting the values,

x + y = 21 ...... equation 1

⟹ 12 + 9 = 21

⟹ 21 = 21

x - y = 3 ..... equation 2

⟹ 12 - 9 = 3

⟹ 3 = 3

Hence, Verified !