You can put this solution on YOUR website! the sum of a two-digit number is 9. the number with the digits interchanged is 6 times the sum of the digits. find the original number
:
Let x = the 10's digit
Let y = the units
then
10x+y = the original number
:
" the sum of a two-digit number is 9."
x + y = 9
:
"the number with the digits interchanged is 6 times the sum of the digits."
10y + x = 6(x + y)
therefore
10y + x = 6(9)
10y + x = 54
:
Arrange to use elimination
x + 10y = 54
x + y = 9
-----------------subtraction eliminates x, find y
9y = 45
y = 45/9
y = 5
:
Find x
x + 5 = 9
x = 4
:
Find the original number: 45
