Finding the original number

Question

The units digit of a two-digit number is one more than twice the tens digit. When the digits are reversed, the new number is 2 more than twice the original number. What is the original number?

Answer 1

Note the value of a two digit number xy is 10x + y

23 = 2(10) + 3

 

Let the 2 digit number be xy

 

The units digit of a two-digit number is one more than twice the tens digit:

y = 2x + 1

 

reversed, the new number is 2 more than twice the original number:

10y + x = 2(10x + y) + 2

10y + x = 20x + 2y + 2

8y - 19x = 2

 

Since y=2x+1, substitute that in and solve for x

8(2x+ 1) - 19x = 2

16x + 8 - 19x = 2

-3x = -6

x = 2

y = 2x+1 = 5

 

The original number xy = 25

Answer 2

Number

tens digit = x

unit digit = 2x+1

 

number = 10(x) +2x+1 =12x+1

 

New Number

tens digit = 2x+1

unit digit =x

New number =10(2x+1)+x =20x+10+x =21x+10

 

New number is 2 more than twice the original number

21x+10 =2(12x+1)+2

21x+10=24x+2+2

21x+10 =24x+4

6 =3x

x=2

 

So

number=12x+1=12(2)+1=24+1=25