Let the number of dimes be $d$, and the number of nickels be $n$.

Step 1: Create equations based on the problem.

We know two things:

1. The value of the nickels and dimes is $1.65, or 165 cents. A nickel is worth 5 cents, and a dime is worth 10 cents. So, the total value can be written as: $5n + 10d = 165$

2. Michael has 6 more nickels than dimes, so: $n = d + 6$

Step 2: Substitute the second equation into the first equation.

Substitute $n = d + 6$ into the first equation: $5(d + 6) + 10d = 165$ Now, simplify and solve for $d$: $5d + 30 + 10d = 165$ $15d + 30 = 165$ Subtract 30 from both sides: $15d = 135$ Divide by 15: $d = 9$

Step 3: Find the number of nickels.

Now that we know $d = 9$, substitute it into $n = d + 6$ to find the number of nickels: $n = 9 + 6 = 15$

Final Answer:

Michael has 15 nickels and 9 dimes.

---

Would you like further details or have any questions about this process?

Here are 5 related questions:

1. How would the solution change if Michael had 10 more nickels than dimes?
2. If the total value of the nickels and dimes was $2.00, how would we solve the problem?
3. What if Michael had the same number of nickels and dimes?
4. How can we use substitution vs elimination methods to solve systems of equations like this one?
5. How would you represent this problem using a system of linear equations?

Tip:

When solving word problems, it’s helpful to define variables clearly, set up equations based on the given conditions, and use substitution or elimination to solve.