https://r2.erweima.ai/mathbot/image/1725416011799kcq6z3qn.jpg

En la figura se muestra una balanza de brazos iguales en la cual se han colocado los
cuerpos, señalados según su forma como, B, C, T y E respectivamente. Los cuerpos
de la misma forma tienen el mismo peso.

4. Con la información que aportan las dos posiciones de la balanza, entonces de las
afirmaciones siguientes, la única de la cual se tiene certeza, con relación al peso de los
cuerpos, es:
a. E > B
b. E > T
c. B > T
d. C > T

5. Si a toda la información inicial se le adiciona la que suministra la nueva posición de la
balanza, entonces, de las afirmaciones siguientes de la única que se tiene certeza es:
a. E < B
b. B > T
c. T < E
d. T > C

### Analyzing the Balances:

#### **First Balance:**
- On the left side: \(\text{T} + \text{C}\)
- On the right side: \(\text{B} + \text{E}\)

The balance tilts downward on the left side, indicating that:
\[
\text{T} + \text{C} > \text{B} + \text{E}
\]

#### **Second Balance:**
- On the left side: \(\text{T} + \text{B}\)
- On the right side: \(\text{E} + \text{E}\)

The balance tilts downward on the right side, indicating that:
\[
\text{E} + \text{E} > \text{T} + \text{B}
\]

### **Question 4: Which statement can be confirmed?**

Given the two observations:
1. From the first balance, \(\text{T} + \text{C} > \text{B} + \text{E}\).
2. From the second balance, \(\text{E} + \text{E} > \text{T} + \text{B}\).

**Let's evaluate each option:**

- **a. \( \text{E} > \text{B} \)**: This might be true since in the second balance, \( \text{2E} > \text{T} + \text{B} \), suggesting \( \text{E} > \text{B} \), but we cannot be certain from the first balance.
- **b. \( \text{E} > \text{T} \)**: This also might be true, but we cannot confirm it without further information.
- **c. \( \text{B} > \text{T} \)**: The second balance suggests the opposite.
- **d. \( \text{C} > \text{T} \)**: From the first balance, \( \text{T} + \text{C} > \text{B} + \text{E} \), but it does not directly compare \( \text{C} \) and \( \text{T} \).

**Conclusion for Question 4**: The only option that can be directly inferred is:
\[
\text{d. } \text{C} > \text{T}
\]

### **Question 5: Which statement can be confirmed with additional information?**

Given the observations:
1. \( \text{T} + \text{C} > \text{B} + \text{E} \)
2. \( \text{E} + \text{E} > \text{T} + \text{B} \)

Adding more information might allow us to evaluate these comparisons more confidently:

- **a. \( \text{E} < \text{B} \)**: This seems unlikely since \( \text{2E} > \text{T} + \text{B} \).
- **b. \( \text{B} > \text{T} \)**: The second balance suggests the opposite.
- **c. \( \text{T} < \text{E} \)**: This is supported by the second balance.
- **d. \( \text{T} > \text{C} \)**: This cannot be confirmed directly.

**Conclusion for Question 5**: The statement that can be confirmed is:
\[
\text{c. } \text{T} < \text{E}
\]

### Follow-Up Questions:
1. How would the results change if the weight of one shape doubled?
2. What conclusions can be drawn if both balances were perfectly level?
3. How can we use algebra to solve for individual weights of B, C, T, and E?
4. What would be the impact on the balance if an additional shape of type E was added?
5. Can we determine the exact weights of the shapes with the given information?

**Tip:** When working with balance problems, always consider using inequalities to set up comparisons between the different sides.

Descubre cómo resolver problemas de balanza de brazos iguales donde se comparan pesos de diferentes cuerpos utilizando desigualdades. Analiza dos situaciones distintas para determinar relaciones de peso entre los cuerpos B, C, T y E. Adecuado para estudiantes de secundaria.

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