Question

Nine times a 2digit number is the same as twice the number obtained by interchanging the digit of number. If one digit of number exceeds the other number by 7.Find the number

Answer 1

let x = the 10's digit
let y = the units
then
10x+y = "the number"
and
10y+x = "the number reversed
:
write an equation for each statement
:
"nine times a two digit number is the same as twice the number obtained on 
interchanging the digits of the number."
9(10x+y) = 2(10y+x)
90x + 9y = 20y + 2x
90x - 2x = 20y - 9y
88x = 11y
simplify, divide by 11
8x = y

;
"If one digit of the number exceeds the other by 7,"
y = x + 7 (y has to be the larger number)
replace y with 8x
8x = x + 7
8x - x = 7
7x = 7
x = 1
then
y = 8
:
18 is the original number