The system of equations provided is:

$D + N = 95$ $0.10D + 0.05N = 7.75$

Where $D$ represents the number of dimes and $N$ represents the number of nickels.

Step 1: Solving the system algebraically

To solve for $D$ and $N$, let's first eliminate one of the variables. We'll use substitution or elimination. For this explanation, let's use substitution.

1. From the first equation: $D + N = 95 \implies N = 95 - D$

2. Substitute $N = 95 - D$ into the second equation: $0.10D + 0.05(95 - D) = 7.75$ Simplify: $0.10D + 0.05(95) - 0.05D = 7.75$ $0.10D + 4.75 - 0.05D = 7.75$ Combine like terms: $0.05D + 4.75 = 7.75$ Subtract 4.75 from both sides: $0.05D = 3$ Solve for $D$: $D = \frac{3}{0.05} = 60$

3. Now that $D = 60$, substitute this into $N = 95 - D$: $N = 95 - 60 = 35$

Thus, the solution is $D = 60$ dimes and $N = 35$ nickels.

Graph interpretation:

The graph shows the intersection of the two lines at the point $(60, 35)$, which aligns with our solution.

Conclusion:

The correct answer is:

• There are about 60 dimes and 35 nickels.

Would you like more details on this solution or how to interpret the graph further?

Here are some additional questions to explore:

1. How would the solution change if the total number of coins was different?
2. What happens if we change the value of one of the coin types (e.g., change nickel to 10 cents)?
3. How could this system of equations be solved using matrices?
4. What if the total amount of money was different (e.g., $10 instead of $7.75)?
5. How can graphing systems of equations help in real-life problem-solving?

Tip: When solving systems of equations, substitution works well when one equation is easy to manipulate for a single variable.