Question

The units digit of a two-digit number is 1 less than the square of the tens digit. The number reversed is 7 more than twice the original number. Find the original number.

Answer 1

" The units digit of a two-digit number is 1 less than the square of the tens digit "

the only possiblities are
10 , 23 , and 38

A quick check,
83 = 2(38) + 7

the original number is 38

or (the long algebraic way)
Let the unit digit be y
let the x digit be x

then y = x^2 - 1
Original number: 10x + y
reversed number: 10y + x

10y + x = 2(10x + y) + 7
19x -8y + 7 = 0
sub in y = x^2 - 1
8x^2 - 19x + 15 = 0
(x-3)(8x-5) = 0
x = 3 or x = a fraction

so x=3, then y= 9-1 = 8

the original number is 38