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The problem is asking for the amount of money Alice received based on the following information:

- Alice and Benny received a total of $100.
- Benny and Catherine received $450 altogether.
- Catherine received five times as much money as Alice.

Let’s define the unknowns:
- Let $ A $ be the amount Alice received.
- Let $ B $ be the amount Benny received.
- Let $ C $ be the amount Catherine received.

We can set up the following system of equations based on the problem:

1. $ A + B = 100 $ (Alice and Benny together received $100).
2. $ B + C = 450 $ (Benny and Catherine together received $450).
3. $ C = 5A $ (Catherine received five times as much money as Alice).

Now, let's solve the system step by step:

### Step 1: Express $ B $ in terms of $ A $
From the first equation, we have:
\[ B = 100 - A \]

### Step 2: Substitute $ B $ in the second equation
Substitute $ B = 100 - A $ into the second equation:
\[ (100 - A) + C = 450 \]
\[ 100 - A + C = 450 \]
\[ C = 450 - 100 + A \]
\[ C = 350 + A \]

### Step 3: Substitute $ C = 5A $ from the third equation
Now, substitute $ C = 5A $ into the equation $ C = 350 + A $:
\[ 5A = 350 + A \]

### Step 4: Solve for $ A $
Subtract $ A $ from both sides:
\[ 4A = 350 \]
\[ A = \frac{350}{4} = 87.5 \]

Thus, Alice received **$87.50**.

Would you like further details or have any questions?

### 5 Related Questions:
1. How much money did Benny receive?
2. How much money did Catherine receive?
3. What would happen if Catherine received 10 times as much money as Alice?
4. How can we verify the solution using all the provided conditions?
5. What if Benny received twice as much as Alice? How would that change the result?

### Tip:
Always check your final answer by substituting back into the original conditions to ensure all equations are satisfied.

Three children shared some money. Alice and Benny received $100 altogether. Benny and Catherine received $450 in all. Catherine received five times as much money as Alice. How much money did Alice receive?

Solve a system of equations to find out how much money Alice received. Alice and Benny received $100 together, and Benny and Catherine received $450. Catherine received five times as much as Alice. Suitable for students in Grades 7-9.

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