How do you find the system???

Question

When you reverse the digits in a certain two-digit number you decrease its value by 18. Find the number if the sum of its digits is 6.

Answer 1

ab=10a+b

ba=10b+a which has a value 18 less than ab

so 10b+a+18=10a+b

a+b=6

b=6-a

10(6-a)+a+18=10a+6-a

60-10a+a+18=9a+6

78-9a=9a+6

78-6=9a+9a

72=18a

a=72/18

a=4, so b=2

42 is the number , 24 is 18 less than 42

this is the work for an algebra 2 student

you could use trial and error if you were in elementary school...

15, 51, 24, 42, 33 are the possible numbers because the digits sum to 6

you can see that 42 and 24 work but not 15 and 51

Answer 2

a + b = 6

10a + b + 18 = 10b + a

9a - 9b = -18

a - b = -2

2a = 4

a = 2

2 + b = 6

b = 4

Let's check.

24 + 18 = 42

42 = 42

0 = 0

Hey hey, sure enough!