To model the given scenario with a system of equations, let's define variables for each type of coin:

• Let $q$ represent the number of quarters.
• Let $n$ represent the number of nickels.
• Let $d$ represent the number of dimes.

From the problem, we know the following:

1. There are 28 coins in total: $q + n + d = 28$

2. The total value of the coins is $3.55 (or 355 cents):

   • A quarter is worth 25 cents.
   • A nickel is worth 5 cents.
   • A dime is worth 10 cents.

   Therefore, the equation for the total value is: $25q + 5n + 10d = 355$

3. There are five times as many nickels as dimes: $n = 5d$

System of equations:

1. $q + n + d = 28$
2. $25q + 5n + 10d = 355$
3. $n = 5d$

Would you like me to solve this system of equations or explain each step further?

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Here are some related questions to think about:

1. How can we simplify the system of equations to make it easier to solve?
2. What happens to the number of nickels and dimes if the total number of coins changes?
3. How would the system change if there were twice as many quarters as dimes?
4. How would the total value equation change if Ms. Wu had pennies instead of dimes?
5. What if there were a restriction on the maximum number of quarters allowed?

Tip: Always look for relationships between variables to reduce the complexity of solving systems of equations.