SOLUTION: The sum of the digits of a two-digit number is 14. If the digits are reversed, the number is 18 less than the original number. Find the original number.
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Question 260211: The sum of the digits of a two-digit number is 14. If the digits are reversed, the number is 18 less than the original number. Find the original number. Found 2 solutions by ankor@dixie-net.com, Alan3354: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
:
10x + y = the original two digit number
:
The sum of the digits of a two-digit number is 14.
x + y = 14
:
"If the digits are reversed, the number is 18 less than the original number."
Rev no. = orig no. - 18
10y + x = 10x + y - 18
10y - y = 10x - x - 18
9y = 9x - 18
simplify, divide by 9
y = x - 2
:
In the sum equation replace y with (x-2)
x + (x-2) = 14
2x = 14 + 2
2x = 16
x = 8
obviously y = 6
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86 is the original number
:
:
Check solution in the statement:
"If the digits are reversed, the number is 18 less than the original number."
68 = 86 - 18
You can put this solution on YOUR website! Swapping digits in a 2 digit number always gives a difference between the 2 numbers of 9 x the difference between the digits.
18/9 = 2
So find 2 numbers whose difference is 2, and whose sum is 14.
x+y = 14
x-y = 2
2x = 16
x = 8
y = 6
--> 86 and 68
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