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:

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.