Final answer:
Alicia has 13 quarters and 65 dimes.
Step-by-step explanation:
Let's set up equations to solve this problem. Let's say Alicia has x quarters. Since Alicia has five times as many dimes as quarters, she would have 5x dimes. The total value of the quarters can be represented as 0.25x (since each quarter is worth $0.25), and the total value of the dimes can be represented as 0.10(5x) (since each dime is worth $0.10).
According to the problem, the sum of the values of the quarters and dimes is $9.75. So we can write the equation:
0.25x + 0.10(5x) = 9.75
Solving for x, we get:
0.25x + 0.50x = 9.75
0.75x = 9.75
x = 9.75 / 0.75
x = 13
Therefore, Alicia has 13 quarters and 65 dimes.