SOLUTION: Please help i totally dont understand how to make this a linear equation that works. The units digit of a two- digit number is less than twice the tens digit. When twice the numb

Question 58422: Please help i totally dont understand how to make this a linear equation that works.
The units digit of a two- digit number is less than twice the tens digit. When twice the number is subracted from 3 times the number formed by reversing the digits of the originaly number, the result is 83. What is the original number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The units digit of a two- digit number is less than twice the tens digit.
:
Say the two digit are x & y, number would be (10x + y)
:
:
When twice the number is subracted from 3 times the number formed by reversing the digits of the original number, the result is 83. What is the original number.
:
twice the number: 2(10x+y);
:
3 times the number reversed: 3(10y+x)
:
3 times reversed number - 2 time original number
3(10y+x) - 2(10x+y) = 83
30y + 3x - 20x - 2y = 83
28y - 17x = 83
:
Using the "try and see" method: Substitute a digit for y, subtract 83 and see
if it is a multiple of 17. I started with 4, then 5, 6 was a success:
6*28 = 168, - 83 = 85 which is multiple of 17. (5*17 = 85)
:
x = 5; y = 6; original number 56:
:
Check: 3(65) - 2(56) = 83
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