Daniel takes pleasure in experimenting with various kinds of toys. He bought three distinct types of toys for $25 in total. Furthermore, he possesses a toy that costs $20 more than three times the combined price of the other two toys. It's revealed that the total cost of the three toys multiplied by five, amounts to $125.
Represent this situation in system of linear equations. 

Let's represent the given situation with a system of linear equations. We'll define the following variables:

- Let $ x $ be the cost of the first toy.
- Let $ y $ be the cost of the second toy.
- Let $ z $ be the cost of the third toy.

Now, let's translate the problem statement into equations:

1. **Total Cost of Three Toys**:  
   The total cost of the three toys is $25.  
   \[ x + y + z = 25 \]

2. **Cost of the Fourth Toy**:  
   Daniel has another toy that costs $20 more than three times the combined price of the other two toys.  
   Let's assume this fourth toy costs $ w $. Then:  
   \[ w = 3(x + y) + 20 \]

3. **Product of Total Cost and 5**:  
   The problem states that the total cost of the three toys multiplied by five is $125.  
   \[ 5(x + y + z) = 125 \]

Now, let's summarize the system of equations:

\[
\begin{aligned}
1) & \quad x + y + z = 25 \\
2) & \quad w = 3(x + y) + 20 \\
3) & \quad 5(x + y + z) = 125 
\end{aligned}
\]

This is the system of linear equations that represents the given problem.

Do you want any further details or have any questions?  
Here are 8 relative questions for deeper understanding:

1. How would you solve the system of linear equations using substitution?
2. How can you use the elimination method to solve this system?
3. What if the toy costs were fractions or decimals? How would that affect the equations?
4. Can you graph these equations to find a visual solution?
5. What is the meaning of each variable in the context of the problem?
6. How does the cost of the fourth toy relate to the others in practical terms?
7. What strategies can you use to check if your solution is correct?
8. Can the problem be extended to include more toys or different conditions?

**Tip:** When dealing with word problems, carefully define your variables and what they represent. This clarity helps in setting up the correct equations.

Learn how to solve a system of linear equations based on a problem involving toy costs. This problem covers key algebraic concepts, including linear equations and word problem strategies. Suitable for students in Grades 7-9.

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