Sergio had 3 times as many books as Davi. After sergio donated 9 books and davi bought another 6 Sergio had 3 more books than Davi. How many books dis Sergio have at first? 

Let's break down the problem step by step to find out how many books Sergio had initially.

1. **Define Variables**:
   - Let \( S \) represent the number of books Sergio had initially.
   - Let \( D \) represent the number of books Davi had initially.

2. **Initial Condition**:
   - According to the problem, Sergio had 3 times as many books as Davi: 
     \[
     S = 3D
     \]

3. **After the changes**:
   - Sergio donated 9 books, so the number of books he had became \( S - 9 \).
   - Davi bought 6 more books, so the number of books he had became \( D + 6 \).
   - After these changes, Sergio had 3 more books than Davi:
     \[
     S - 9 = (D + 6) + 3
     \]

4. **Set Up the Equation**:
   - Simplify the equation from the final condition:
     \[
     S - 9 = D + 9
     \]
   - Add 9 to both sides to isolate \( S \):
     \[
     S = D + 18
     \]

5. **Substitute and Solve**:
   - We already know from the initial condition that \( S = 3D \). Substituting this into the equation \( S = D + 18 \), we get:
     \[
     3D = D + 18
     \]
   - Subtract \( D \) from both sides:
     \[
     2D = 18
     \]
   - Divide by 2:
     \[
     D = 9
     \]
   - Now substitute \( D = 9 \) back into the equation \( S = 3D \):
     \[
     S = 3(9) = 27
     \]

6. **Conclusion**:
   - Sergio initially had **27 books**.

Would you like to see the details of any step, or do you have any questions?

Here are five related questions:
1. If Sergio had donated 12 books instead of 9, how many books would he have initially?
2. What if Davi bought 10 more books instead of 6, how would that change the outcome?
3. How many books would Davi have after his purchase and Sergio's donation?
4. If the initial ratio between Sergio's and Davi's books was 4:1, what would the initial numbers be?
5. How would the result change if Sergio donated only 5 books?

**Tip**: When working with word problems, clearly defining your variables and breaking down the steps methodically can help you avoid mistakes.

Explore the solution to Sergio and Davi's book problem, where Sergio initially had 3 times as many books as Davi. After Sergio donated 9 books and Davi bought 6 more, Sergio ended up with 3 more books than Davi. Learn how to solve this word problem step-by-step. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation