Verbal question problem help I had this question today and I got confused on how to construct my solution for this. At the first view of the question, I decided to use $X$ and $Y$ and no other option:
Maria purchased $X$ books for 300 dollars. After a day, the shop sold the books for 2 dollars cheaper. So Ana purchased 10 books more than Maria, and each book costed dollar 2 less than the original price. Ana paid 350 for her books.
How many books Maria purchased, and how much each costed?
I structured  my 2 equations like this:
${X \cdot Y = 300}$
$(X + 10) \cdot (Y - 2) = 350$
Did I build my two equations correctly according to the question? How can I solve it? because when I solve it, I get $-Y^2 = 640$ and then I get totally lost not knowing if I did that right.
My steps:
$X = 300 - Y$
$((300 - Y) + 10)(Y - 2) = 350$
$=> (3000 -10Y)(Y - 2) = 350 => 3000Y - 6000 - 10Y^2 - 20Y = 350$
Now idea what to do from this step...
 A: Your mistake is in this step: $(X−2)⋅(Y+10)=350$
It should be ideally $(X+10)⋅(Y-2)=350$
The second equation uses the variables appropriately chosen by you and will even give the correct result.
Your step first should be  $X=300/Y$ 
A: As I mentioned in my comment, the first step should be $X=300/Y$. But that will make it hard to solve. A better way is to look at your second equation. If you multiply it out, there is a term $XY$ which can be replaced with $300$ according to your first equation. You might then go on to do your substitution with this simplified step.
Also you should be careful when doing the algebra. I noticed several mistakes in your steps. For example $(300-Y)+10 \ne 3000 -10Y$, and so on.
A: Maria bought X books for 300 dollars.
So cost of each book $=\frac{300}{X}.$
After that the prices were reduced by 2 dollars per book.
So Ana bought $(X+10)$ books for 350 dollars.
So, cost of each book $=\frac{350}{X+10}.$
According to the problem,
$\frac{300}{X}-2=\frac{350}{X+10}.\\or, \frac{150}{X}-1=\frac{175}{X+10}.\\or,\frac{150}{X}=\frac{175}{X+10}+1.\\or,\frac{150}{X}=\frac{185+X}{X+10}.\\or,150(X+10)=X(185+X).\\or, 150X+1500=185X+X^2.\\or,X^2+35X+1500=0.\\or, (X+60)(X-25)=0.$
This gives either $X=-60$  or  $X=25$ .
Since number of books purchased cannot be negative,  the valid solution is   $X=25$  .
So Maria bought $25$ books and cost of each book was $\frac{300}{25}=12$  dollars .
