A two Digit number is 1 more than 8 times the sum of the digits. The ones digit is 3 less than the tens digit. What is the number?

Question

Linear Equantions 

Answer 1

lets suppose a two numbers as x and y with y being the ones and x being the tens.

 

Now, multiplying the numbers by its place,

x*10+y*1=8(x+y)+1

 

Another equation

y+3=x

 

Substituting the value of x in the first equation,

you get y=1

then, x=4

 

Answer 2

A two digit positive integer can be written as

10(tens digit) + (ones digit).  Example:  37 = 10(3) + 7.

 

Let x= tens digit and let y = ones digit.

 

Then 10x + y = 8(x + y) + 1 and y = x - 3.

 

Simplifying, we arrive at the system:

 

2x  - 7y = 1

          y = x - 3

 

Replace y by x - 3 in the first equation to get 2x -7(x - 3) = 1.

 

So, 2x - 7x + 21 = 1

 

     -5x = -20.  Therefore, x = 4 and y = x - 3 = 1

 

Answer:  the number is 41