I am not sure that I completely understand the first part of your question, but...

57 is 18 less than 75, which is the the digits reversed.

5+7=12 12x3=36 36 is 24 more than 12, which is the sum of 5+7.

No, it's 46. Units digit is only the 2nd number, not the sum of the numbers.

4+6=10
10x3= 30
30-24 = 6 (the units digit)

64-46= 18

yes nice job leeroy

Yep.

If you need to show work, this is how I solved it:

The original number is n.

To represent n as 2 separate digits, I just used n=xy and wrote the equation in terms of x and y.

By the stipulations set forth in the first sentence, you can write: y = 3(x+y) - 24

That simplifies as: y = -(3/2)x + 12

The original number is only 2 digits and by looking at the leading coefficient of x (-(3/2)), you should realize that each x is a factor of 2. In fact, there are only 4 possible combinations of x and y: 29, 46, 63, & 80. Reverse the digits and viola, 64 is 18 more than 46.

There's a more rigorous explanation, and you can actually pull out the pattern for each digit. Hint: 2, 4, 6, 8 = all possible variations of x | 9, 6, 3, 0 = all possible variations of y.

you can use a more straight forward approach.

first of all represent the number you are looking for in terms of its digits, i.e. 10a+b with a being the first digit ("ten's place") and b being the second digit ("one's place").

now you write your information into equations.

the units digit (b in our case) is 24 less then three times the sum of the digits (a+b).

->I: b=3*(a+b)-24

if the digits are reversed, the new number (10b+a) is 18 more than the original number (10a+b).

->II: 10b+a=10a+b+18

equation II looks easier to solve, so we start with that one. we subtract 1a and 1b on both sides.

II: 9b=9a+18

and divide by 9

II: b=a+2

inserting that into equation I yields

a+2=3*(a+a+2)-24

simplifying that leads to

a=4 and since a=b-2 (II) b=6

=> the two digit number is 46.

(+487 for 1st and +451 for dominance)
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dr. zoidberg 69 finishes 1st in round 15

shit nice, my best is still jjust 750 i cant farm with all these ppl complaining