Justin has $3.25 worth of dimes and quarters. He has a total of 16 dimes and quarters altogether. Determine the number of dimes and the number of quarters that Justin has.

We are given the following information:

- Justin has a total of 16 coins, consisting of dimes and quarters.
- The total value of the coins is $3.25, which is equivalent to 325 cents.

Let:
- $ d $ be the number of dimes.
- $ q $ be the number of quarters.

We can set up two equations based on the problem:

1. The total number of coins:
\[
d + q = 16
\]
2. The total value of the coins (since each dime is worth 10 cents and each quarter is worth 25 cents):
\[
10d + 25q = 325
\]

### Step 1: Solve the system of equations

From the first equation, solve for $ d $ in terms of $ q $:
\[
d = 16 - q
\]

### Step 2: Substitute into the second equation

Substitute $ d = 16 - q $ into the second equation:
\[
10(16 - q) + 25q = 325
\]

Simplify the equation:
\[
160 - 10q + 25q = 325
\]
\[
160 + 15q = 325
\]

### Step 3: Solve for $ q $

Subtract 160 from both sides:
\[
15q = 165
\]

Divide by 15:
\[
q = 11
\]

### Step 4: Solve for $ d $

Now, substitute $ q = 11 $ into the first equation:
\[
d + 11 = 16
\]
\[
d = 5
\]

### Conclusion:
Justin has 5 dimes and 11 quarters.

Would you like more details or have any questions?

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Here are some related questions to extend your understanding:

1. If Justin had 20 coins instead of 16, how would that change the solution?
2. How can you check the solution to ensure it's correct?
3. How would the problem change if Justin had $4.75 instead of $3.25?
4. How can you solve similar problems using matrices?
5. How would the problem change if there were nickels instead of dimes?

**Tip:** When solving word problems, always set up equations based on the relationships given in the problem to keep track of all conditions!

Determine how many dimes and quarters Justin has based on the total value of $3.25 and the total number of 16 coins. This solution uses algebraic methods such as setting up systems of linear equations and applying substitution. Ideal for students in Grades 6-8.

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