https://file.aiquickdraw.com/mathbot/file/1729793722576vu4tdd3p.jpg

The problem from the image asks to determine the individual weights of Ida, Ada, and Eva based on the following information:

- Ida and Ada together weigh 124 kg.
- Ida and Eva together weigh 118 kg.
- Ada and Eva together weigh 130 kg.

Let's denote the weights of Ida, Ada, and Eva as \( I \), \( A \), and \( E \), respectively. From the problem, we can set up the following system of equations:

\[
I + A = 124 \quad \text{(1)}
\]
\[
I + E = 118 \quad \text{(2)}
\]
\[
A + E = 130 \quad \text{(3)}
\]

### Step-by-step solution:
1. **Add all three equations:**
   \[
   (I + A) + (I + E) + (A + E) = 124 + 118 + 130
   \]
   Simplifying the left side:
   \[
   2I + 2A + 2E = 372
   \]
   Divide the entire equation by 2:
   \[
   I + A + E = 186 \quad \text{(4)}
   \]

2. **Use equation (4) to find individual weights:**
   From equation (4), we know:
   \[
   I + A + E = 186
   \]
   Now, subtract each of the original equations from this:

   - Subtract equation (1) \( (I + A = 124) \) from \( (I + A + E = 186) \):
     \[
     E = 186 - 124 = 62
     \]

   - Subtract equation (2) \( (I + E = 118) \) from \( (I + A + E = 186) \):
     \[
     A = 186 - 118 = 68
     \]

   - Subtract equation (3) \( (A + E = 130) \) from \( (I + A + E = 186) \):
     \[
     I = 186 - 130 = 56
     \]

### Final Answer:
- Ida weighs 56 kg.
- Ada weighs 68 kg.
- Eva weighs 62 kg.

Would you like any additional explanation, or do you have further questions?

---

Here are 5 related questions for further exploration:
1. How can this method be applied to solve other systems of equations with three variables?
2. What happens if the sum of the weights did not add up perfectly (e.g., with decimal values)?
3. How would you approach this problem if there were four people instead of three?
4. Can you solve this system using matrix algebra?
5. How does this type of problem relate to real-life situations, such as balancing weights?

**Tip:** Whenever you solve systems of equations, adding all equations together is a quick way to find the sum of all variables.

Ida, Ada, and Eva need to weigh themselves, but the scale only works for people weighing over 100 kg. They decide to weigh two at a time: Ida and Ada weigh 124 kg together, Ida and Eva weigh 118 kg together, and Ada and Eva weigh 130 kg together. What is the individual weight of each person?

Learn how to solve a system of linear equations to find the individual weights of Ida, Ada, and Eva. This problem involves calculating weights given their pairwise sums and is suitable for students in Grades 6-8. Step-by-step solution included.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation