Well first of all I am not a mathematician, but I enjoyed assimilating the basic principles of math.
Considering the problem as follows:
"Bob and Alice have 10 candies in total, and Bob has 2 more candies than Alice. How many candies do Bob and Alice each have?"
My own solution would be to just define the variables as follows:
Bob = Alice + 2;
Bob + Alice = 10;
2xAlice + 2 = 10;
Alice = (has) 4 candies;
Bob = (has) 6 candies.
Adjusting the problem with an odd difference instead of an even number we have:
"Bob and Alice have 10 candies in total, and Bob has 3 more candies than Alice. How many candies do Bob and Alice each have?"
Bob = Alice + 3;
2xAlice + 3 = 10;
Alice = (has) 3.5 candies;
Bob = (has) 6.5 candies.
I find my solution to be easier to understand and somehow more logical than "let's add/substract this and that and divide by two". Probably my main issue was explaining to a kid how having 3.5 and 6.5 candies works seeing candies I known all my life are basically unbreakable (unless you have a kid's teeths which is known to be able to devour metal).
As an anecdote I recently dated a lady who has a teenage daughter and she showed me the math exams her youngling has been taking. Having never been one to withdraw from a challenge, even mildly implied, I printed the things and started working on them only to be horrified how much I've forgotten in terms of elementary mathematics. I genuinely felt shame even though I scored a decent number (but nothing to write home about).
I feel we're failing our children in how we're pumping them with information but without always teaching them how to learn and that makes me really sad :(
10-3 / 2 = 3.5 candies for Bob.
You may think that's a strange solution, but it's the only one that matches the problem statement. What was your solution?