A jar contain 500 gold and silver coins. Each gold coin is valued at $11.00 while each silver coin is valued at $2.00. If the total monetary value in the jar is $4150.00, which of the following can be used to model the information if x represents the number of gold coins and y represents the number of silver coins?


To model the situation with variables $ x $ and $ y $, where:
- $ x $ represents the number of gold coins.
- $ y $ represents the number of silver coins.

### Step 1: Formulate the Equations

**Equation 1: Total Number of Coins**
- The total number of coins is given as 500.
\[
x + y = 500
\]

**Equation 2: Total Monetary Value**
- The value of each gold coin is $11.00.
- The value of each silver coin is $2.00.
- The total value of the coins is given as $4150.00.
\[
11x + 2y = 4150
\]

### Step 2: System of Equations
The situation can be modeled using the following system of linear equations:
\[
\begin{align*}
x + y &= 500 \quad \text{(Equation 1)} \\
11x + 2y &= 4150 \quad \text{(Equation 2)}
\end{align*}
\]

This system of equations represents the problem and can be solved simultaneously to find the values of $ x $ and $ y $.

Would you like to solve this system of equations, or do you have any questions?

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Here are 8 related questions to expand your understanding:
1. How do you solve a system of linear equations using substitution?
2. How do you solve a system of linear equations using elimination?
3. What does the solution of the system represent in this context?
4. How would the system change if the value of each gold coin was different?
5. What would happen if the total monetary value was less than $4150.00?
6. How can you check the solution to the system of equations?
7. What other methods can be used to solve this system of equations?
8. How would you interpret a situation where no solution exists for the system?

**Tip:** When working with systems of linear equations, it's useful to clearly define each variable and ensure that your equations are consistent with the context of the problem.

Learn how to model a problem involving 500 gold and silver coins using systems of linear equations. Understand the relationship between the number of coins and their monetary value, with detailed steps and examples. Suitable for students in Grades 9-12.

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