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

Answer:

The Original Number is 36

Step-by-step 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.

$10y+x=27+10x+y\\10y-y+x-10x=27\\9y-9x=27\\9(y-x)=27\\y-x=\frac{27}{9}$

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

Adding equation 1 and 2 we get

$(x+y=9)+(y-x=3)\\2y=12\\y=\frac{12}{2}\\y= 6$

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 = $10x+y=10\times3+6=30+6=36$