Final answer:
Violet has 10 nickels and 11 dimes.
Step-by-step explanation:
To determine the number of nickels and dimes Violet has, we can set up a system of equations.
Let's say she has x nickels and y dimes.
We know that the total value of nickels is $0.05 * x and the total value of dimes is $0.10 * y.
Since Violet has a total of 21 nickels and dimes altogether, we can write the equation:
x + y = 21.
We also know that the total value of nickels and dimes is $1.60, so we can write the equation:
0.05x + 0.10y = 1.60.
Using the first equation, we can solve for x:
x = 21 - y.
Substituting this into the second equation, we get:
0.05(21-y) + 0.10y = 1.60.
Distributing, we have: 1.05 - 0.05y + 0.10y = 1.60.
Combining like terms, we get: 0.05y = 0.55.
Dividing both sides by 0.05, we find that y = 11.
Substituting this back into the equation x = 21 - y, we get:
x = 21 - 11 = 10.
Therefore, Violet has 10 nickels and 11 dimes.