A bag contains n nickels and q quarters worth a total of $40.Which equation models this information?n+q=405n+25q=400.5n+0.25q=400.05n+0.25q=40

To model the given information about nickels and quarters in a bag worth a total of $40, we will break it down as follows:

1. Break Down the Problem

We need to represent the total value of nickels and quarters using a mathematical equation. We have:

• n: the number of nickels
• q: the number of quarters
• The value of a nickel is $0.05 (or 5 cents).
• The value of a quarter is $0.25 (or 25 cents).
• The total value of nickels and quarters is $40.

2. Relevant Concepts

We know from the problem statement that:

• The value of all nickels is $0.05n$
• The value of all quarters is $0.25q$

The equation that represents the total monetary value will be: $0.05n + 0.25q = 40$

3. Analysis and Detail

We can rearrange the equation to ensure it is in a standard format. Multiplying every term by 100 to get rid of the decimals: $5n + 25q = 4000$

However, this form is not needed since the original equation $0.05n + 0.25q = 40$ essentially conveys the same information directly.

4. Verify and Summarize

Looking at the given options:

• $n + q = 405$ (This does not represent the total value)
• $5n + 25q = 400$ (This is incorrect given our calculations)
• $0.5n + 0.25q = 400$ (Also incorrect format for values)
• $0.05n + 0.25q = 40$ (Correct equation)

Final Answer

Thus, the correct equation that models the information is: $\boxed{0.05n + 0.25q = 40}$