Learn English – difference between someone was ill vs someone became ill

The penny is the coin, and cent refers to how much the penny is worth.

If I told you I had 15 cents, that could be three nickels, or a dime and five pennies, or two nickels and five pennies (there are other possible combinations as well).

Since she already mentioned the dime, it makes sense that she also said "pennies" instead of "cents." I suppose she might have said:

I have a dime plus four more cents

That would be grammatical, but usually we speak of coins with coins and cents with cents.

Had you asked me the same question, and I had the same amount of money, I'd probably say either of these:

I have a dime and four pennies.

or

I only have fourteen cents.

I might lean toward the first wording if you asked me about currency:

Do you have a quarter?
No, I only have a dime and four pennies.

but the second if you asked me about money:

How much money do you have?
On me? Only fourteen cents.

One other possibility, if I had to count my money in order to answer your question (in other words, I knew I has some coins in my pocket, but didn't remember what they were), then I might say it like she did:

How much money do you have?
On me? Let me see. [pulls five coins from pocket] I've got a dime.... and four pennies.

I'd assume you could do the math as easily as I could, so I wouldn't bother to state the sum.

Assuming that graduate application means applying for a higher degree in an academic institution, each can make sense depending on what you really have:

Aspirations - If you can paint this long-term vision of how getting this degree will change your life because then you'll be able to do X,Y, and Z then this would be an aspiration. Eliminating world hunger would be an example here of a big picture idea. I want there to be world peace would be another example often heard at beauty pageants.

Goal - If you can give a much more specific idea of what you plan to do after completing the program that would reflect well upon the institution. Eliminating hunger in your city by following the plans outlined in a proposal would be an example here that is fairly localized specific and would be done over the short-term. I want to end bullying in this school would be another example where the key is how specific is the objective.