Tristan has $1.40 worth of nickels and dimes. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Tristan has. Define the variables that you use to write the system.

To solve this problem, we need to set up a system of equations using two variables:

1. Let $ n $ represent the number of nickels Tristan has.
2. Let $ d $ represent the number of dimes Tristan has.

### Given information:
- Tristan has twice as many nickels as dimes, which gives us the first equation:
  \[
  n = 2d
  \]
- The total value of the nickels and dimes is $1.40. Since each nickel is worth 5 cents and each dime is worth 10 cents, we can express the total value of the coins as:
  \[
  5n + 10d = 140
  \]
  (We use 140 cents instead of $1.40 to avoid decimals.)

### System of Equations:
\[
\begin{cases}
n = 2d \\
5n + 10d = 140
\end{cases}
\]

This system of equations can be solved to determine the number of nickels $ n $ and dimes $ d $.

Do you want me to solve the system or explain any specific step further? 

Here are 5 questions related to this problem:
1. What methods can be used to solve this system of equations?
2. How do we translate word problems into mathematical equations?
3. What are the common strategies for solving systems of equations?
4. Can this problem be solved using substitution or elimination?
5. What if Tristan had three times as many nickels as dimes? How would the system change?

**Tip:** Always convert dollars to cents when dealing with coin-related word problems to avoid working with decimals.

Learn how to set up a system of equations to solve for the number of nickels and dimes Tristan has, given he has $1.40 and twice as many nickels as dimes. This problem explores key algebraic concepts, including coin value problems and systems of equations, suitable for students in Grades 6-8.

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