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If 18 is added to a two-digit numbers, the digits are reversed. the sum of the digit is 8. What is the original number?

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Posted on Oct 12, 2008

  • Ken Newberg Oct 12, 2008

    sorry. number would have to be 35.

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I don't think you can do it! Could you check your numbers.

If we are using the numbers 1-9 once and only once in a 3x3 magic square, the sum of the rows + the sum of the columns should be 90, since 1+2+3+4+5+6+7+8+9 in the rows adds up to 45 and 1+2+3+4+5+6+7+8+9 in the columns adds up to 45.

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The sum of the digits of a two-digit number is 14. if the digit is reversed, the number is increased by 18. what is the number?


a 2 digit number is a tens place digit plus a singles place digit:
10x + y

if you reverse the 2 digits, it looks like:
10y + x

So, the original 2-digit number, plus another 18, gets the 2nd 2-digit number:

10x + y + 18 = 10y + x

AND adding the 2 digits gets 14:
x+y = 14

Solve for x: x = 14-y

Substitute x back into the previous equation and solve for y:

10 (14 - y) + y + 18 = 10y + (14 - y)

140 - 10y + y + 18 = 10y + 14 -y

158 - 9y = 9y + 14

144 - 9y = 9y

144 = 18y

y = 8

So if y = 8, x must equal 6: x+ y = 14 --> 6 + 8 = 14

And the original number, 68, if you reverse the digits --> 86

86 is 18 greater than 68.

I love math!

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