Translation:She is looking for fifteen pesos in the purse.
According to several sources, "your purse" should/can be "la cartera." (It depends on your country -- Mexico does NOT use the definite article.)
Try to get over the idea that there's a "proper" Spanish. There's a current Spanish in Spain, and a current Spanish in Latin America (and regional variations within Latin America, and there probably are in Spain, too.) Aspects of the Spanish in Spain today are likely different than they were at the time of American colonisation. Everything's always changing everywhere.
It would be nice if Duolingo had separate streams for Spanish and Latin America, though. Before the internet, most language training programs (which came on phonograph records and later on cassettes and CDs) had separate versions.
I was wondering if this construction without the personal pronoun is similar to the way Spanish uses the definite article rather than possessive pronoun for body parts. For instance, "I broke my leg" = me rompí la pierna. It would be incorrect to use mi pierna, but is a common mistake for people acquiring Spanish whose first language uses the personal pronoun in that phrase. Long story short, I think la cartera here is idiomatic and translates as "her purse" in English which prefers the pronoun (although as others have pointed out "the purse" here does work). But the question here is how Spanish works. Whether some forms of Spanish (e.g., Argentina, El Salvador, Mexico) use the pronoun in this case is beyond my knowledge and experience. I would wonder if the pronoun is used in some Spanish speaking countries or regions whether it is from interference from English. But as always I defer to native speakers of Spanish to let us know what is idiomatic in their region. In my region of US English, we "get ready" or "are about to" go some place, but in some parts of the southern US they "are fixin" to go some place.
It seems like a waste of time to overthink this one. It's pretty simple. It might not be what is "natural" to say, or what someone "would say". "la cartera" = "the purse". It could be la casa, la sala, el carro, el cuarto. They're not telling you a story, they're just giving you a sentence to translate. If you got it wrong, don't worry, you'll get another chance to get it right.
Obviously, your learning was incomplete. See these references:
But, they do not use the same peso. For example 1 Colombian peso is not worth the same as 1 Mexican peso or 1 Argentine peso. So, you need to say which peso you are talking about. They are not the same just because they use the word, "peso". It is the same for dollars. There are Canadian and US dollars, but they are have different values and the bills and coins do not look the same. There are also Cayman dollars and Bahamian dollars, but they have nothing to do with US dollars or Canadian dollars.
The peso is the unit of currency in Mexico, just like the dollar is the unit of currency in the USA.
If you wrote "Ella busca 15 pesos en la cartera", it marked you wrong because you completely defeated the purpose of the lesson, which is to teach you the number in Spanish, which is "quince".
If you tried to write "She is looking for 15 pesos in the purse" and it marked you wrong, you very likely had an error somewhere in the sentence. Next time, copy and paste the full text of your answer so we can see what's going on.
It could indeed be translated as either "she looks" or "she is looking". If the Spanish really wanted to emphasize that she is looking in the purse right now, there's a tense called present progressive that looks like "ella está buscando". Spanish does have many different tenses but doesn't always use them exactly the same way English does, e.g. English uses the present-progressive ("she is looking") more freely than Spanish does.