Question

Let x and y represent the tens digit and ones digit of a two digit number, respectively. The sum of the digirs of a two digit numbet is 9. If the digits are reversed, the new number is 27 more than the original number. What is the original number? *Write a system of equations *solve the systems of equations

Answer 1

The Original Number is 36

Explanation:

Given:

y is the number in units place

x is the number in tens place

Original Number =
`10x+y`

`x+y=9` is equation 1

Now after interchanging the digits

New number =
`10y+x`

New Number = 27 + Original Number

Substituting Valus in above equation we get.

`10y+x=27+10x+y\\10y-y+x-10x=27\\9y-9x=27\\9(y-x)=27\\y-x=(27)/(9)\\`

`y-x=3` let this be equation 2

Adding equation 1 and 2 we get

`(x+y=9)+(y-x=3)\\2y=12\\y=(12)/(2)\\y= 6\\`

Substituting value of y in equation 1 we get

`x+y=9\\x+6=9\\x=9-6\\x=3`

x=3 and y=6

Original Number =
`10x+y=10*3+6=30+6=36`