Question

The sum of to numbers is 69. If one number is seven more than the other, find the numbers.

Answer 1

Given :

• Sum of two numbers = 69
• One number is seven more than the other.

To Find:

• The required numbers.

Solution :-

Let the one number be x.

Then, the other number = x+7

According to question,

$: \implies {\sf{x +( x + 7) = 69}} \\ \\ : \implies {\sf{x +x + 7 = 69}} \\ \\ : \implies {\sf{2x+ 7 = 69}} \\ \\ : \implies {\sf{2x = 69 - 7}} \\ \\ : \implies {\sf{2x = 62}} \\ \\ : \implies {\sf{x = \cancel{\dfrac{62}{2} }}} \\ \\ : \implies{ \boxed {\tt{x = 31}}}$

$\therefore{\underline{\sf{One \: number =\bf{31}}}}$

$\therefore{\underline{\sf{Other \: number =31+7\bf{=38}}}}$

Verification :

We have,

• Sum of two numbers = 69
• One number = 31
• Other number =38

Subsituating the values :

$: \implies {\sf{31 +38 = 69}} \\ \\ : \implies {\sf{69 = 69}} \\ \\ : \implies{ \boxed {\tt{ LHS=RHS}}}$

$\therefore{\underline{\bf{Verified.}}}$

Answer 2

Answer :

➥ The numbers = 31 and 38

Given :

➤ Sum of two numbers = 69

➤ One number is seven more than the other$.$

To Find :

➤ Number = ?

Required Solution :

In the above Question, we have to find the number whose sum is 69. So, firstly we have to consider the number as an variable, and accordingly the other number. Then, we can frame equation to get the result of x.

Let ,

Let the one number be "x" and the other number be "x+7"

So let's start solving the equation and understand the steps to get our final result for x.

Sum of two numbers = 69

⇛ x + (x + 7) = 69

Get rid of unnecessary parentheses,

⇛ x + x + 7 = 69

Calculate between similar terms,

⇛ 2x + 7 = 69

Move the constant to right side and change the sign,

⇛ 2x = 69 - 7

Subtract 7 from 69,

⇛ 2x = 62

Divide both by the same number,

⇛ x = 62/2

Divide 62 by 2,

⇛ x = 31

Now ,

⇛ One number = x

⇛ One number = 31

⇛ Other number = x + 7

⇛ Other number = 31 + 7

⇛ Other number = 38

║Hence, the other number is 31 and 38.║

Verification :

››› Sum of two numbers = 69

››› 31 + 38 = 69

››› 69 = 69

Here, LHS = RHS.

❮ Hence Verified ❯