Example 1
She gave me half of her money so that I could have my dance lessons.
Example 2
She gave me half of her money so that I was able to have my dance lessons.
What is the difference between "could" and "was able to" here?
Does "could" mean that it became possible for me to have dance lessons?
Does "was able to" mean that I successfully had dance classes?
I would say they are the same, both indicating that 'she' provided money (likely at hardship to herself) that allowed the speaker/writer to take dance lessons.
The "was able to" might be seen as slightly more formal, but in this instance I would say that difference is razor thin.
"Can" is tricky because it is a very old word which can be replaced by different modern words, and has different meanings in different context.
In the example you give, "could" is the past tense of "can", which can be replaced by "was able to". They mean the same thing, but "can" is older and shorter; "was able to" is more modern and verbose.
I give some examples of this in the previous question: "can" or "could"- general possibility
A lot of it has to do with the development of the philosophical exploration of the concept of "will". We needed new and clearer ways to talk about things happening to go with our developed understanding of making things happen.
Does "could" mean that it became possible for me to have dance lessons?
Yes. It became possible for you to have dance lessons after getting half her money.
Does "was able to" mean that I successfully had dance classes?
No. You could have taken the money and spent it on something else instead. It became possible for you to have dance lessons after getting half her money, but it does not mean that you have successfully completed the lessons.
"She gave me half of her money, which I used to take dance lessons." is one of the ways to say that you have successfully completed what was made possible.
Hope this helps :)
She gave me half of her money so that I could have my dance lessons.
This sentence means that someone (let's call them Person A) was very generous and made it possible for you to take dance lessons. (You might not have taken them at the time of speaking.)
IMO, your next sentence is incorrect and needs to be fixed. If you want to use "was able to", it will have a different meaning as we use this form to refer to an ability on a specific occasion. British Council
She gave me half of her money, so I was able to have my dance lessons.
The sentence uses "was able to" which implies you actually had the dance lessons (ability on a specific occasion). Unlike "could", "was able to" focuses on a completed action.
“Can” in English is a so-called defective verb, meaning it can’t be conjugated in all the same ways as other verbs. We use “be able” as a replacement for “can” in these situations (e.g. “I will be able to”, not *”I will can”). In addition, you can also use “be able” in those situations where “can” itself (or its conjugated forms) can also be used.
In this case, “could” is the past tense of “can”, and “was able” is the past tense of “be able”, and there is no appreciable difference in meaning.
