# math

posted by .

when you reverse the digits of the number 13,the number increases by 18.how many other 2digit numbers increase by 18 when their digits are reversed ?

• math -

let the unit digit be x and the tens digit be y
then the number is 10y + x
and the number reversed would be 10x + y
but 10x + y - (10y + x) = 18
9x - 9y = 18
x-y = 2

this works for:
3,1 ---> our given case
4,2
5,3
6,4
7,5
8,6
and 9,7

check 7,5
if x=7, y = 5
the original number was 57
number reversed 75
and 75 - 57 = 18
The text passage contains a mathematical question about finding how many two-digit numbers increase by 18 when their digits are reversed, and it provides a detailed solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# math

posted by .

when you reverse the digits of the number 13,the number increases by 18.how many other 2digit numbers increase by 18 when their digits are reversed ?

• math -

let the unit digit be x and the tens digit be y
then the number is 10y + x
and the number reversed would be 10x + y
but 10x + y - (10y + x) = 18
9x - 9y = 18
x-y = 2

this works for:
3,1 ---> our given case
4,2
5,3
6,4
7,5
8,6
and 9,7

check 7,5
if x=7, y = 5
the original number was 57
number reversed 75
and 75 - 57 = 18
user
The text passage contains a mathematical question about finding how many two-digit numbers increase by 18 when their digits are reversed, and it provides a detailed solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER