Help Math problem !!!! Math test tommrow! ( step by step please)?

A

ahfiujh

New member
Translate into system of eqations and solve:

* The sum of digits of a two-digit number is 12. If you reverse the digits, the new number is 36 greater than the original number. Find the original number.
 
Let's name the first digit of the number t and the second digit n. Now understand that the VALUE of the number is 10t+n.
From the first sentence the SUM of the digits, not the number's value is t+n=12
"if you reverse the digits" is different than the sum of the digits because it takes in account the place value. So for that part it means 10n+t
with the rest of the second sentence you have 10n+t=36+ 10t+n
now put alike terms together. 9n-9t=36. By taking out a 9, that simplifies to n-t=4
now you can use elimination using that simplified equation and the n+t=12
the t's cancel out leaving 2n=16, n=8 making t=4
Your number then is 48

let me know if you need some elaboration!
 
These I just kind of do in my head. So first, I envision everything that would add up to 12.
i.e. 66, 39, 93, 48, 84, etc.
Then I just look at the next step. The new number is 36 greater. So firstly, we know that the new number is bigger, which means the old number must have been small, meaning it might be 39, or 48. If we add 36 to these, 48 is the one that gives you 84.

GOOD LUCK ON YOUR TEST. :)
 
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