Assume the total amount of problems is $100$ per half homework assignment, since we are dealing with percentages, and not values.  Then, we know that Chloe got $90$ problems correct by herself, and got $120$ problems correct overall.  We also know that Zoe had $70$ problems she did correct alone.  We can see that the total amount of correct problems Chloe and Zoe did was $120-90=30$. Therefore Zoe has $30+70=100$ problems out of $200$ problems correct. Thus $\frac{100}{200} = 50$ percent. 
Chloe and Zoe are both students in Ms. Demeanor\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to $90\textbackslash\%$ of the problems she solved alone, but overall $60\textbackslash\%$ of her answers were correct. Zoe had correct answers to $70\textbackslash\%$ of the problems she solved alone. What was Zoe\textquotesingle s overall percentage of correct answers? (adapted from 2017 AMC 8, Question \#14) 

1. $$45$$ 
2. $$48$$ 
3. $$50$$ 
4. $$60$$ 
5. $$65$$ 