SOLUTION: the units digit of a two digit number is one less than one half the tens digit. the number with the digits interchanged is 5 more than thrice the sum of the digits. find the origin
Question 1132113: the units digit of a two digit number is one less than one half the tens digit. the number with the digits interchanged is 5 more than thrice the sum of the digits. find the original number. (use only one variable) (thanks in advance) Found 2 solutions by Theo, josgarithmetic:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! let x = the tens digit.
then x/2 - 1 = the units digit.
the number would be 10 * x + (x/2 - 1) originally.
with the digits inter-changed, the number becomes 10 * (x/2 - 1) + x.
simplify this to get 5*x - 10 + x.
combine like terms to get the number with the digit inter-changed = 6x - 10.
the number with the digits inter-changed is equal to 5 plus 3 times the sum of the digits.
that becomes 6x - 10 = 5 + 3 * (x + x/2 - 1)
simplify to get 6x - 10 = 5 + 3x + 3x/2 - 3
3x + 3x/2 becomes 9x/2.
equation becomes 6x - 10 = 5 + 9x/2 - 3
combine like terms to get 6x - 10 = 2 + 9x/2
multiply both sides of this equation by 2 to get 12x - 20 = 4 + 9x
add 20 to both sides of this equation and subtract 9x from both sides of this equation to get 3x = 24.
solve for x to get x = 8.
x is the tens digit.
the units digit is x/2 - 1 = 3
the number is 83.
when you inter-change the digits, the number becomes 38.
38 = 3 * the sum of the digits + 5 which becomes 3 * 11 + 5 = 38
solution looks good.
the original number is 83.
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