Final Answer:
The system of inequalities for Madelyn's coins can be represented as 0.25x + 0.10y ≤ 3.60 (as the combined value of quarters and dimes should be at most $3.60) and x + y ≥ 18 (since she has no less than 18 coins). Solving this graphically reveals one possible solution where x = 12 quarters and y = 6 dimes meet both conditions simultaneously.
Step-by-step explanation:
Madelyn's situation can be expressed using two inequalities. The first inequality represents the combined value of her coins, where the quarters' worth (each worth $0.25) added to the dimes' worth (each worth $0.10) must be at most $3.60. This inequality is expressed as 0.25x + 0.10y ≤ 3.60, where x represents the number of quarters and y represents the number of dimes.
The second inequality accounts for the total number of coins Madelyn possesses. She must have no fewer than 18 coins in total, expressed as x + y ≥ 18, as stated in the problem.
To find a solution, graph these inequalities on a coordinate plane, marking the feasible region where both conditions are satisfied. In this case, one possible solution within this region could be x = 12 quarters and y = 6 dimes. This combination of coins not only respects the value restriction (0.25(12) + 0.10(6) = $3.60) but also satisfies the coin count condition (12 quarters + 6 dimes = 18 coins).
Through this graphical method, it's possible to find multiple combinations of quarters and dimes that meet the criteria given. However, the specific solution of 12 quarters and 6 dimes is just one of the potential valid combinations that adhere to the constraints provided.