Question

The units digit of a two-digit number is 3 and seven times the sum of the digits is the number itself. Find the number.​

Answer 1

Given :

• The units digit of a two-digit number is 3.

• Seven times the sum of the digits is the number itself.

To calculate :

• The number.

Calculation :

Let the two digit number be 10a + b.

⪼ $\bf { a = Tens \: digit}$

⪼ $\bf { b = Units \: digit}$

Now, as per the given question the digit of a two-digit number is 3 and seven times the sum of the digits is the number itself. So, we'll form an algebraic equation and by solving that equation we'll find that two digit number.

According to the question :

➛ $\bf {Units \: digit = 3}$

➛ $\bf {b = 3}$

Also,

➛ 7 × sum of the digits = Number

➛ $\bf {7(a+b) = 10a +b}$

➛ $\bf {7a + 7b= 10a +b}$

➛ $\bf { 7b-b= 10a-7a }$

➛ $\bf { 6b= 3a }$

Substituting value of b :

➛ $\bf { 6(3) = 3a }$

➛ $\bf { 18= 3a }$

➛ $\bf { \dfrac{18}{3} = a }$

➛ $\boxed{\bf { 6= a }}$ ★

Hence,

➨ $\bf { a = 6}$

➨ $\bf { b = 3}$

Therefore, original number :

➛ $\bf { Original \: Number = 10a + b }$

➛ $\bf { Original \: Number = 10(6) + 3 }$

➛ $\bf { Original \: Number = 60 +3 }$

➛ $\underline{ \boxed { \pmb { \rm \red { Original \: Number = 63 }}}}$

Therefore, the number is 63.

Answer 2

Answer:

Let the tens place be X .

the units place digits is 3 .

therefore - > Number = ( 10x + 3 )

Given

7 ( x + 3 ) = ( 10x + 3 )

7 x + 21 = 10x + 3

Therefore - > 10x - 7x = 21 - 3

= > 3 x = 18

or x = 6

using x = 6 in equation ( 1 ) ..

The number is 63 .

Step-by-step explanation: