Final answer:
To find the number of nickels and dimes, set up two equations based on the total value of the coins and the total number of coins. Solve the equations to find the values of x (nickels) and y (dimes).
Step-by-step explanation:
To solve the problem, we can set up two equations.
The first equation represents the total value of the nickels and dimes: 0.05x + 0.10y = total value (in dollars).
The second equation represents the total number of coins: x + y = 22.
We can rearrange the second equation to solve for x: x = 22 - y.
Then, substitute this value of x into the first equation to solve for y: 0.05(22 - y) + 0.10y = 1.60.
Simplify and solve for y to find the number of dimes, and then substitute this value back into the equation x = 22 - y to find the number of nickels.