Question

7th grade math question. A number consists of two digits whose sum is 8. If 18 is added to the number its digts are reversed. Find the number ​​​

Answer 1

Answer:

Let one digit of the number be x , then its ten digits digits will be (8−x) .

digits digits will be (8−x) .

$\sf \: So , given \: number =10(8−x)+x </p><p> </p><p>$

$⠀⠀⠀⠀⠀⠀⠀⠀ </p><p> =80−10x+x$

[tex⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

=80−9x[/tex]

Now if digits are reversed , then Number obtained

⠀⠀⠀⠀⠀⠀⠀⠀ \: =10x+(8−x)

                                \:  =10x+8−x

                                \:  =9x+8

[/tex]

$\red \:according \: to \: question$

$(80−9x)+18=9x+8$

$\sf   98−9x=9x+8$

$90=18x$

$\sf \: given \: number  =80−9x$

$⠀⠀⠀⠀⠀⠀⠀⠀⠀=80−9×5$

$⠀⠀⠀⠀⠀⠀⠀⠀⠀=80−45$

$⠀⠀⠀⠀⠀⠀⠀⠀⠀=35$

Answer 2

Given,

• A number consist of two digit whose sum is 8.

if 18 is added, the number gets reversed.

Solution:-

Let the 1st digit be x

2nd digit = 8-x

According to Question,

10x+(8-x) +18= 10(8-x) + x Now let's solve this equation

9x+26=80-10x+x

9x+26=80-9x

9x+9x=80-26

18x=54

$x = \frac{54}{18}$

x=3

We got the first digit 3,

second digit= 8-3= 5

Original digit=35

Verification:-

10(3) +(8-3)+18

=30+5+18

=35+18

=53

And, 35+18=53

Condition check

•Adding 18 to the number reverses the digit ✔️

•Sum of digits =3+5=8 ✔️