SOLUTION: The digit in the tens place of a two-digit number is four more than twice the digit in the ones place. The new number obtained by reversing the order of the digits of the original

Question 1117034: The digit in the tens place of a two-digit number is four more than twice the digit in the ones place. The new number obtained by reversing the order of the digits of the original number is 54 less than the original number. Use a system of equations in two variables to find the original number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
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