https://file.aiquickdraw.com/mathbot/file/1726732986217mqeiqrq3.jpg

Let's go through the questions one by one and match them to the given equations.

### 1. **Christophe buys 3 notebooks, and Emilie buys 4. Together, they spend 7 euros. What is the price of one notebook?**
   Let the price of one notebook be \( x \). We know that Christophe buys 3, and Emilie buys 4, so:
   \[
   3x + 4x = 7
   \]
   This matches equation **b)**: \( 7x = 7 \).

### 2. **A steel ball and a 4 kg lead ball together weigh the same as 3 balls. What is the mass of one ball?**
   Let the mass of one ball be \( x \). The total mass of one steel ball and the 4 kg lead ball is the same as three balls, so:
   \[
   x + 4 = 3x
   \]
   This matches equation **c)**: \( x + 4 = 3x \).

### 3. **An equilateral triangle and a square have sides of the same length. The perimeter of the square is 7 meters more than that of the triangle. What is the length of the side of the square and the triangle?**
   Let the side length of both the square and the triangle be \( x \). The perimeter of the square is \( 4x \) and the perimeter of the triangle is \( 3x \), and we know the square's perimeter is 7 meters more than the triangle's:
   \[
   4x = 3x + 7
   \]
   This matches equation **d)**: \( 3x + 7 = 4x \).

### 4. **Find the number such that its triple increased by 7 is equal to its quadruple decreased by 3.**
   Let the number be \( x \). We are told that three times the number, plus 7, equals four times the number, minus 3:
   \[
   3x + 7 = 4x - 3
   \]
   This matches equation **d)**: \( 3x + 7 = 4x - 3 \).

### 5. **Here is the rule of a game:**
   - **When you win, you receive 4 €.**
   - **When you lose, you give 3 €.**
   Emilie played 7 times and won 7 € in total. How many times did she win?

   Let \( x \) be the number of wins, and since she played 7 times, the number of losses is \( 7 - x \). Her total earnings are given by:
   \[
   4x - 3(7 - x) = 7
   \]
   This matches equation **e)**: \( 4x + 3x = 7 \).

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Let me know if you would like further clarification or detailed steps for any of these solutions!

### Five related questions:
1. How do you solve simple linear equations like \( 3x + 4x = 7 \)?
2. What are the key steps in solving word problems involving systems of equations?
3. How can you verify the solution to an equation once you've found it?
4. How would the problem change if Christophe and Emilie spent 10 euros instead of 7?
5. Can you generalize a method for solving perimeter-related problems for different shapes?

### Tip:
Always carefully define your variables and units at the start of a word problem. It helps to clearly set up the equation and avoid confusion later!

The original math exercises, including solving linear equations and word problems.

This webpage covers how to solve linear equations and word problems, including exercises on purchasing notebooks, calculating masses, finding side lengths of geometric shapes, and solving for unknowns. Ideal for students in Grades 6-8 looking to strengthen their algebra and geometry skills.

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