How many 2-digit whole numbers are increased by 18 when their digits are reversed?

Question

blurbendy · Answer

To represent a 2-digit whole number we can write that as:

10t + u
where t represents "tens" and u represents "ones"

Then we can add 18 because that's what the question says:

(10t+u) + 18

to represent the reverse we just include the opposite of 10t + u, which is 10u + t

(10t+u) + 18 = (10u+t)

solve:

 10t+u+18 = 10u+t

9t-9u+18 = 0

t - u + 2 = 0

u = t + 2

If t = 1, u = 3, then 13 is a solution
Can you figure out the rest?

If t = 2, u = 4
If t = 3, u = 5
If y = 4, u = 6 
If y = 5, u = 7
If y = 6, u = 8
If y = 7, u = 9

perl · Answer

nice solution :)