https://file.aiquickdraw.com/mathbot/file/1729156797235shw7t70g.jpg

Let's solve the problem step by step.

Let:
- $ D_0 $ represent Dewi's initial amount of money.
- $ L_0 $ represent Lu Di's initial amount of money.

### Step 1: Set up the relationship before they spend any money.
According to the problem, Lu Di had 2 times as much money as Dewi initially. Thus:
\[
L_0 = 2D_0
\]

### Step 2: Set up the relationship after they both spent $66.
After a month, both Lu Di and Dewi spent $66 each. So, the amount of money they have left is:
- Lu Di: $ L_0 - 66 $
- Dewi: $ D_0 - 66 $

At this point, Lu Di has 5 times as much money as Dewi:
\[
L_0 - 66 = 5(D_0 - 66)
\]

### Step 3: Solve the equation.
Substitute $ L_0 = 2D_0 $ into the second equation:
\[
2D_0 - 66 = 5(D_0 - 66)
\]

Expand the equation:
\[
2D_0 - 66 = 5D_0 - 330
\]

Move all terms involving $ D_0 $ to one side and constants to the other:
\[
2D_0 - 5D_0 = -330 + 66
\]
\[
-3D_0 = -264
\]

Solve for $ D_0 $:
\[
D_0 = 88
\]

### Step 4: Find $ L_0 $.
Since $ L_0 = 2D_0 $:
\[
L_0 = 2 \times 88 = 176
\]

### Final Answer:
Lu Di initially had **$176**.

Would you like more details or clarifications?

Here are 5 related questions to explore:
1. What if Lu Di had 3 times as much money as Dewi initially?
2. How would the solution change if they spent a different amount of money?
3. Can you generalize the relationship for any multiplier between Lu Di's and Dewi's money?
4. What would happen if Dewi had initially more money than Lu Di?
5. How does solving this problem help with understanding linear equations?

**Tip:** When setting up equations from word problems, clearly define variables and relationships to avoid confusion.

Lu Di had 2 times as much money as Dewi. After a month, both of them spent $66 each. Then, Lu Di has 5 times as much money as Dewi. How much money did Lu Di have at first?

Learn how to solve a problem involving linear relationships between two people spending money. This step-by-step solution involves setting up algebraic equations and solving for the initial amounts. Suitable for Grades 7-9.

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