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Question 521530: Three times the ten digit of a certain two-digit number is two more than four times the units digit. The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits. Find the number.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let x = the 10's digit
Let y = the units
then
10x+y = "certain number"
:
Write an equation for each statement:
:
"Three times the ten digit of a certain two-digit number is two more than four times the units digit."
3x = 4y + 2
3x - 4y = 2
:
" The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits."
(10x+y) - (10y+x) = 2(x+y) - 2
10x + y - 10y - x = 2x + 2y -3
9x - 9y = 2x + 2y - 2
9x - 2x - 9y - 2y = -2
7x - 11y = -2
:
Use these two simplified equations for elimination
Mult the 1st by 7, mult the 2nd by 3
21x - 28y = 14
21x - 33y = -6
----------------subtraction eliminates x, find y
0 + 5y = 20
y = 20/5
y = 4
:
Use 3x = 4y +2, replace y with 4
3x = 4(4) + 2
3x = 18
x = 18/3
x = 6,
then
64 is the number
:
:
Check this in the statement:
" The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits."
64 - 46 = 2(6+4) - 2
18 = 2(10) - 2
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