Let's denote the number of quarters Len received as $q$ and the number of dimes as $d$.

We have two key pieces of information:

1. The total number of coins: $q + d = 6$

2. The total amount of money in change: $0.25q + 0.10d = 1.35$

Step 1: Solve the System of Equations

First, we'll solve the first equation for one of the variables, say $q$: $q = 6 - d$

Step 2: Substitute into the Second Equation

Next, substitute $q = 6 - d$ into the second equation: $0.25(6 - d) + 0.10d = 1.35$

Step 3: Simplify and Solve for $d$

Expanding the equation: $1.50 - 0.25d + 0.10d = 1.35$

Combine like terms: $1.50 - 0.15d = 1.35$

Subtract 1.50 from both sides: $-0.15d = -0.15$

Divide both sides by -0.15: $d = 1$

So, Len received 1 dime.

Step 4: Find the Number of Quarters

Substitute $d = 1$ back into the equation $q = 6 - d$: $q = 6 - 1 = 5$

So, Len received 5 quarters.

Final Answer:

Len received 5 quarters and 1 dime.

Would you like more details or have any questions?

Here are five related questions:

1. How can you use a system of equations to solve problems involving two unknowns?
2. What other methods can be used to solve systems of linear equations besides substitution?
3. How do we convert between different denominations of money in mathematical problems?
4. How can you set up an equation to solve problems involving combinations of coins?
5. What are some real-life situations where systems of linear equations might be used?

Tip: When solving word problems, carefully define your variables and write down the information given in the problem as equations. This helps in organizing the solution process.