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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

User Domenica
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1 Answer

2 votes

Answer:

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

User Roman Melnyk
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