# 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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## Related Questions:

### The Sum of 2 integers from 1 to 9 that are four consecutive numbers. Show that either one or three of the numbers on the counters were even

I need some help here. If we take the sum of 2 integers from 1 to 9, and they can be the same number, the maximum number is 18. I don't know how you are supposed to get four consecutive digits, unless you pad the number with zeros. Am I missing something?

Good luck,

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### I'm trying to figure out a 3x3 magic square where the rows equal 21 18 10 and the columns equal 15 24 13 using the numbers 1-9

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.

When trying to solve, the magic number seem to be the sums 24 and 10. To get 24, the only three numbers that add to 24 are 7 + 8 +9. Similarly to get 10, the lowest numbers re 1 and 2 and the smallest big number to use is 7. I then ran out of number trying to get 21, 13 and 15 sums.

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A number is 3 more than 4 the sum of its digits. If the digits are interchanged, the resulting number is 9 more than the given number. Find the number.

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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!

Sep 01, 2009 | Google Computers & Internet

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