PROBLEM 1. Radu and Alexandra have 11 lei together. They decide to buy a book together, contributing equal amounts of money. Radu has to borrow 1 leu from Alexandra, and after buying the book, Alexandra is left with 5 lei.

a) Find the price of the book;

b) How many lei did Alexandra have initially?
PROBLEM 1. Radu and Alexandra together have 11 lei. They decide to buy a book together, contributing equal amounts of money. Radu has to borrow 1 leu from Alexandra, and after buying the book, Alexandra is left with 5 lei.

a) Find the price of the book;

b) How many lei did Alexandra have initially?

Grading criteria. Algebraic method (alternatively, figurative method):

(2p) a) The price of the book is $11-5=6$ lei.

$(3 p)$ b) Let $R$ be the amount of money Radu has and $A$ be the amount of money Alexandra has. Since $R+A=11$ and $R+1=A-1-5$,

(2p) we get $A=R+7$, from which we find that $R=2$ and $A=9$.