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...

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.
