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Let's work through this system of equations to solve for the number of coins Maverick has.

The three equations provided are:
1. $ 0.25q + 0.10d + 0.05n = 2 $ (this represents the total value of the coins in dollars)
2. $ q + d + n = 15 $ (this represents the total number of coins)
3. $ 6d = q $ (this comes from the fact that there are 6 times as many quarters as dimes)

Now, you're asked to substitute the expression for $ q $ from the third equation into the first two equations.

The third equation is already solved for $ q $:
\[
q = 6d
\]

### Step 1: Substitute $ q = 6d $ into the first equation:
\[
0.25(6d) + 0.10d + 0.05n = 2
\]
Simplifying this:
\[
1.5d + 0.10d + 0.05n = 2
\]
\[
1.6d + 0.05n = 2 \quad \text{(This is the new form of the first equation)}
\]

### Step 2: Substitute $ q = 6d $ into the second equation:
\[
6d + d + n = 15
\]
Simplifying this:
\[
7d + n = 15 \quad \text{(This is the new form of the second equation)}
\]

### The rewritten system of equations:
1. $ 1.6d + 0.05n = 2 $
2. $ 7d + n = 15 $

These are the equations you should work with now. Would you like to proceed with solving these equations, or do you have any questions so far?

Here are 5 relative questions you can explore:
1. How can we solve the system of equations we just derived?
2. What would happen if Maverick had twice as many quarters as dimes?
3. How would the system of equations change if the total number of coins was different?
4. Can we solve this system of equations using substitution or elimination?
5. How does the relationship between the value of different coins impact the overall solution?

**Tip:** In word problems, converting verbal descriptions into algebraic expressions systematically can simplify the solving process significantly.

Maverick has 15 coins in his pocket, made up of quarters, nickels, and dimes. The total value of the coins is $2, and he has 6 times as many quarters as dimes. How many of each coin does Maverick have in his pocket?

Learn how to solve a system of equations where Maverick has 15 coins worth $2, consisting of quarters, nickels, and dimes. This problem covers key algebraic concepts such as substitution and solving for multiple variables. Suitable for students in Grades 8-10.

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