Vincent bought a few books at an average price of $20 each. When he bought another bag which cost $59, the average price of all the books and the bag became $23. How many books did Vincent buy?

Answer 1

Let's assume Vincent bought $x$ books.
The total cost of the books is $20x.
After buying the bag, the total cost of the bag and books is $20x+59.
The average price of all the books and the bag is $23.
According to the information above, the equation is $\frac{20x+59}{x+1}=23$.
The equation can be rewritten as $20x+59=23(x+1)$.
Multiplying out the brackets gives $20x+59=23x+23$.
Subtracting 20x and 23 from both sides gives $36=3x$.
Thus, $x=\frac{36}{3}=12$.
Therefore, Vincent bought a total of 12 books. Answer: \boxed{12}.