The valid set of equations (0.25q + 0.05n = 3.65 and q + n = 20) that accurately represent the problem's conditions. Here option D is correct.
Let's define:
- q as the number of quarters,
- n as the number of nickels.
The value of a quarter is $0.25, and the value of a nickel is $0.05.
The total number of coins is given as 20, so we have the equation: q + n = 20.
The total value of the coins is $3.65, so we have the equation: 0.25q + 0.05n = 3.65.
A. 0.059 + 0.25n = 20 - This equation doesn't make sense. The left side does not represent a valid expression for the total number of coins.
B. 0.05q + 0.25n = 2.85 - This equation doesn't match the total value equation. The correct total value equation is 0.25q + 0.05n = 3.65, not 0.05q + 0.25n = 2.85. Therefore, option B is incorrect.
C. 0.25g + 0.05n = 20 - There's a variable g that is not defined in the problem. This is not a valid equation, so option C is incorrect.
D. 0.25q + 0.05n = 3.65 and q + n = 20 - This set of equations correctly represents the problem. The first equation accounts for the total value, and the second equation represents the total number of coins. Therefore, option D is correct.