Question

A number consists of two digits. The sum of the digits is 12. If 18 is added to the number, the digits
are reversed. Find the number.
with only one variable​

Answer 1

Answer:

You meant “the digits are reversed; what is the original number?”

The solution can be obtained by letting x be the ‘tens digit’, and y be the unit digit, so that the original number is 10x+y.

Then 10x+y+18=10y+x, because the digits are reversed. This simplifies to 9x+18=9y, or x+2=y. Since the digits add up to 12, x+y=12. Substituting for y yields x+2=12-x, which simplifies to x=5. Then y=7, so the original number is 57. 57+18 = 75.

You’re asking what is the sum of the digits is if 18 is added to the original number. If the new number is a 2 digit number, the sum is still 12, but if it spills into 3 digits, the sum changes (84+18=102; sum is 3).

I’m pretty sure you meant #1, but i’m trying to be thorough.

Answer 2

Answer:

57

Step-by-step explanation:

let tens digit be x then tens digit 12-x

original no. = 10x+12-x

=9x+12

if 18 is added then no.

9x+12+18= 10(12-x)+x

9x+30=120-10x+x

9x+9x=120-30

18x=90

x=90/18

x=5

then original number = 9*5+12

= 45+12

=57