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A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. find the number ​

Answer 1

$\boxed{\boxed{\frak{\orange{QuEsTion}}}}$

A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digit are reversed . find the  number.

$\boxed{\boxed{\frak{\orange{AnsWer}}}}$

Let, the tens digit of no. = x

and ones digit  = y

then, the actual  no. = 10 x + y

and reversed no. = 10 y + x

According to condition I

actual number = 3 + 4 ( x + y )

10 x + y = 3 + 4 x + 4 y

6 x - 3 y - 3 = 0

( dividing by 3 both sides we will get)

$\bf 2x-y-1=0\\\\\boxed{\bf y=2x-1}.....eqn(1)$

According to condition II

reversed number = ( actual no.) + 18

10 y + x = 10 x + y + 18

9 y - 9 x - 18 = 0

(dividing by 9 both sides we will get)

$\bf y - x - 2 = 0$

(putting eqn(1))

$\bf 2x-1-x-2=0\\\\\bf x-3=0\\\\\boxed{\bf x = 3}$

putting value of x in eqn(1)

y = 2 x - 1

y = 2 (3) - 1

$\boxed{\bf y = 5}$

Hence, the actual number will be

10 x + y

= 10 ( 3 ) + 5

$\large{\bf = 35}$

$\frak{\orange{The\:actual\:no.\:is\:35.}}$

Answer 2

Answer:

35

Step-by-step explanation:

10x+ y= 4(x+y) + 3

10x + y = 4x + 4y + 3

10x - 4x + y - 4y =3

6x - 3y = 3

3(2x - y) = 3

2x - y = 1 -> 1

also, 10x + y + 18 = 10y + x

10x + y - 10y - x = -18

9x - 9y = 18

x - y = 2 -> 2

from 1 and 2

2x - y = 1

x - y = 2

_________

x = 3 ( subtracting we get)

substituting value of x in equation 1 we have

2*3 - y = 1

-y = - 5

y = 5

therefore xy=35