SOLUTION: The tens' digit of a certain two-digit number is twice the units' digit. The difference between the square of the number and the square of the number obtained by reversing the digi

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: The tens' digit of a certain two-digit number is twice the units' digit. The difference between the square of the number and the square of the number obtained by reversing the digi      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 181909: The tens' digit of a certain two-digit number is twice the units' digit. The difference between the square of the number and the square of the number obtained by reversing the digits is 297. What is the number?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The tens' digit of a certain two-digit number is twice the units' digit.
The difference between the square of the number and the square of the number
obtained by reversing the digits is 297. What is the number?
:
Let x = 10's digit
Let y = units digit
then
10x + y = the two-digit number
:
Write an equation for each statement:
:
"The tens' digit of a certain two-digit number is twice the units' digit."
x = 2y
:
" The difference between the square of the number and the square of the number obtained by reversing the digits is 297."
(10x-y)^2 - (10y-x)^2 = 297
:
(100x^2 - 20xy + y^2) - (100y^2 - 20xy + x^2) = 297
:
100x^2 - 20xy + y^2 - 100y^2 + 20xy - x^2 = 297
:
100x^2 - x^2 - 20xy + 20xy + y^2 - 100y^2 = 297
:
99x^2 - 99y^2 = 297
:
simplify, divide equation by 99
x^2 - y^2 = 3
:
Substitute 2y for x
(2y)^2 - y^2 = 3
:
4y^2 - y^2 = 3
;
3y^2 = 3
:
y^2 = 3%2F3
:
y^2 = 1,
Therefore
y = 1 and x = 2: 21 is the number
:
:
Check
21^2 - 12^2 =
441 - 144 - 297