Question

Suppose Santiago bought 34 books. Can you figure out how many of each type of book he bought? Explain

Answer 1

I don’t have enough information to give a definite answer — you need to tell me the extra conditions (prices, total cost, how many types, or any other relations between the numbers). As stated, “Santiago bought 34 books” by itself has infinitely many integer solutions.

If you paste the full problem I’ll solve it exactly. Meanwhile here is the method I’d use and a short example so you can see how it works.

General method
- Let variables x, y, z, ... be the number of each type of book (non‑negative integers).
- Write one equation for the total number of books: x + y + z + ... = 34.
- Write any other equations or constraints given (for example, a total cost equation or ratio constraints).
- Solve the linear system (substitute to reduce the number of variables). Because counts must be integers ≥ 0 you will usually end up checking only a small range of integer possibilities (use modular arithmetic or bounds to narrow it).
- Pick the integer solution(s) that satisfy all constraints.

Short illustrative example
Suppose the problem were: “Santiago bought 34 books. He bought novels for $3 each and textbooks for $5 each, and he spent $140 total. How many of each did he buy?”

Let n = novels, t = textbooks.
1) n + t = 34
2) 3n + 5t = 140

From (1) n = 34 − t. Substitute in (2):
3(34 − t) + 5t = 140 → 102 − 3t + 5t = 140 → 2t = 38 → t = 19 → n = 15.

So he bought 15 novels and 19 textbooks.

Give me the full original problem (prices, extra totals or relations, number of types) and I’ll solve it exactly for Santiago.