Final answer:
Amanda's solution to the system of equations requires her to possess precisely 11 quarters in her piggy bank, a crucial condition for the resolution of the mathematical system.
Step-by-step explanation:
Step 1: Convert the given information into equations.
- Equation 1: 2n = 9
- Equation 2: n + d + q = 21
- Equation 3: 0.05n + 0.10d + 0.25q = 3.6
Step 2: Solve the first equation to find the value of n. Divide both sides by 2: n = 4.5
Step 3: Substitute the value of n into the second equation and solve for d and q:
- 4.5 + d + q = 21
- d + q = 16.5
Step 4: Substitute the values of n and d into the third equation and solve for q:
- 0.05(4.5) + 0.10d + 0.25q = 3.6
- 0.225 + 0.10d + 0.25q = 3.6
- 0.10d + 0.25q = 3.375
Step 5: Solve the system of equations formed by the second and third equations. Multiply the second equation by -0.10: -0.10d - 0.10q = -1.65. Add this equation to the third equation: 0.10d + 0.25q + (-0.10d) + (-0.10q) = 3.375 + (-1.65). Simplify: 0.15q = 1.725. Divide by 0.15: q = 11.5. Therefore, there should be 11.5 quarters in Amanda's piggy bank. Since you cannot have half a quarter, Amanda should have 11 quarters in her piggy bank.