Question

a two digit number has a tenth digit x and a units digit y. (for example, 72 has a tenth digit 7 and a units digit 2.) the sum of the two digits is 7. when the digits are reversed, the resulting number is less than the original number by 27. (in the case of 72, the sum of its digits is 9 and when the digits are reversed, the resulting number is 27 which is less than the original number by 45.) what is the original two-digit number?

Answer 1

52

Explanation:

let the two digits be x and y;

xy

x+y=7

when the numbers are reversed yx=10y+x

10x+y-(10y+x)=27

9x-9y=27 divide both sides by 9;

x-y=3

lets form a system of equation and solve;

x+y=7

x-y=3

subtract the two equations;

2y=4

y=2

substitute 2 in the equation to find x

x=5

the number is 52