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We are given that:

- The total number of coins is 26.
- The coins are dollar coins and quarters.
- The total value is 17 dollars.

Let:
- $ x $ be the number of dollar coins.
- $ y $ be the number of quarters.

We have two pieces of information that translate into equations:

1. The total number of coins:
\[
x + y = 26
\]

2. The total value in dollars (dollar coins are worth 1 dollar, and quarters are worth 0.25 dollars):
\[
x + 0.25y = 17
\]

Now we can solve this system of equations.

### Step 1: Solve the first equation for $ x $:
\[
x = 26 - y
\]

### Step 2: Substitute $ x = 26 - y $ into the second equation:
\[
(26 - y) + 0.25y = 17
\]
Simplifying:
\[
26 - y + 0.25y = 17
\]
\[
26 - 0.75y = 17
\]
\[
0.75y = 9
\]
\[
y = \frac{9}{0.75} = 12
\]

### Step 3: Solve for $ x $:
\[
x = 26 - 12 = 14
\]

Thus, there are **14 dollar coins** and **12 quarters**.

Let me know if you'd like a further breakdown, and here are some related questions to explore:

1. How would the solution change if you had a total of 30 coins instead of 26?
2. What if the total value was $18 instead of $17?
3. How could this problem be modeled graphically?
4. What other combinations of coin types would change the system of equations?
5. How would you set up the system if some coins were dimes instead of quarters?

**Tip**: When solving systems of equations, always check the units of each term (like dollars or coins) to ensure the equations make sense!

The twenty-six coins in my pocket are all dollar coins and quarters, and they add up to seventeen dollars in value. How many dollar coins and how many quarters are in my pocket?

Learn how to solve a system of equations problem where 26 coins, consisting of dollar coins and quarters, add up to $17. This problem covers key algebraic concepts such as linear equations and systems of equations. Suitable for students in Grades 7-9.

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