Maths puzzle please help

[XxLucyxx]

13+25=?? 16+28=35 19+31=38 that's all the info I have

 

[stapel]

13+25=?? 16+28=35 19+31=38 that's all the info I have

Any mathematical formula that you can logically justify should be a valid answer. That said, "the" right answer is whatever the author had in mind.

The fact that the part that you're supposed to fill out comes first suggests that order is an issue. Using number bases (here), I've noted the following for the last equation:

. . . . .19₁₀ + 31₁₀ = 50₁₀

That is to say, in base-10 numbers, the "equality" is not true. However:

. . . . .50₁₀ = 38_?

That is to say, the "answers" may be equal in some other number base. What happens if we subtract eight 1's from either side?

. . . . .42₁₀ = 30_?

Now we have 42, in base-10, being equal to three "tens" of whatever number base. Divide through by 3:

. . . . .14₁₀ = 10_?

In other words, the "38" was actually 42, but written in base-14:

. . . . .19₁₀ + 31₁₀ = 1*14 + 5 + 2*14 + 3 = 3*14 + 8 = 38₁₄

What happens with the middle equation?

. . . . .16₁₀ + 28₁₀ = 44₁₀

. . . . .44₁₀ = 35_?

. . . . .39₁₀ = 30_?

. . . . .13₁₀ = 10_?

The middle equation is in base-13, which is one less than the last equation, which was base-14.

. . . . .16₁₀ + 28₁₀ = 1*13 + 3 + 2*13 + 2 = 3*13 + 5 = 35₁₃

Should we assume that the pattern follows, that the first equation is meant to be done with base-12? This seems reasonable, so see what you can find.