溶ける and 溶かす: melting and dissolving ingredients
Compare ingredients melting with those dissolving in liquid, checking particles for the result and the action.
A change of form under heat
暖かい部屋でチョコレートが溶けました。 says that chocolate melted in a warm room. With 溶ける, read とける, the melting ingredient is the subject.
チョコレートを溶かして、型に入れました。 says that someone melted chocolate and put it in a mold. 溶かす, read とかす, describes making the ingredient melt.
An ingredient dissolves in water
砂糖がお湯に溶けました。 says that sugar dissolved in hot water. Distinguish dissolving in water from heating sugar itself until it melts.
砂糖をお湯に溶かしてください。 asks someone to dissolve sugar in hot water. 砂糖を is the ingredient, and お湯に is the liquid it goes into.
Remaining grains and another とける
よく混ぜましたが、まだ全部は溶けていません。 says that someone stirred it well, but it has not all dissolved yet. Stirring is an action; complete dissolution is a separate result.
問題が解けました。 can describe managing to solve a problem or its being solved. It shares the reading but uses 解, unlike 溶ける for ingredients melting or dissolving.
Does 砂糖がお湯に溶けました describe heating sugar without water?
Show the answer and why
No. The sugar dissolved in hot water. お湯に explicitly identifies the liquid it dissolved in.