Question 1117034
let a = the 10's digit
let b = the units
:
Write an equation for each statement:
The digit in the tens place of a two-digit number is four more than twice the
 digit in the ones place.
a = 2b + 4
 The new number obtained by reversing the order of the digits of the original number is 54 less than the original number.
10a + b = 10b + a + 54
10a - a = 10b - b + 54
9a = 9b + 54
simplify, divide by 9
a = b + 6
:
 Use a system of equations in two variables to find the original number.
a = a, therefore
2b + 4 = b + 6
2b - b = 6 - 4
b = 2
find a
a = 2 + 6
a = 8
:
Original number 82
:
;
Check in the statement
"The new number obtained by reversing the order of the digits of the original number is 54 less than the original number."
82 = 28 + 54