Question

The sum of two numbers is 13 One number is 7 more than the other one. Find the numbers.

Answer 1

Answer:

13-7=6

so the other number is 6.

Answer 2

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

Here, as per the given question we are provided that the sum of two numbers is 13 and one number is 7 more than the other one. We have to find those two numbers.

We'll first assume those numbers as variables, say x and y.After that, we'll form algebraic equations and by solving that equations, we'll find the value of those numbers.

$\Large {\underline { \sf \orange{Explication \: of \: Steps :}}}$

Let the numbers be x an y respectively.

According to the question,

$\longrightarrow \sf { {Sum}_{(Two \: Numbers)} = 13 }$

$\longrightarrow \sf { x + y = 13 }$ . . . . .⑴

Also,

$\longrightarrow \sf { Number_{(First)}= 7 + Number_{(Other \: one)} }$

$\longrightarrow \sf { x = 7 + y}$ . . . . ⑵

Substitute the value of x in equation ⑴ to find the value of y.

$\longrightarrow \sf { x + y = 13 }$

$\longrightarrow \sf { (7 +y) + y = 13 }$

$\longrightarrow \sf { 7 +y + y = 13 }$

$\longrightarrow \sf { 7 + 2y = 13 }$

$\longrightarrow \sf { 2y = 13 -7 }$

$\longrightarrow \sf { 2y = 6 }$

$\longrightarrow \sf { y =\cancel{ \dfrac{6}{2} }}$

$\longrightarrow\boxed{ \sf \orange { y =3 }}$

Now, substitute the value of y in equation ⑵ to find the value of x.

$\longrightarrow \sf { x = 7 + 3}$

$\longrightarrow\boxed{ \sf \orange { x = 10 }}$

Therefore,

$\bigstar \boxed{ \sf \orange { One \: Number = 3 }}$

$\bigstar \boxed{ \sf \orange { Another \: Number = 10 }}$

$\Large {\underline { \sf \orange{Verification :}}}$

As per the asked question,

• Sum of two numbers is 13.

$\longrightarrow \sf { x + y = 13 }$

L.H.S :

$\longrightarrow \sf { 10 + 3 }$

$\longrightarrow \sf { 13 }$

R.H.S :

$\longrightarrow \sf { 13 }$

Therefore, L.H.S = R.H.S

Hence, verified !