Final answer:
To solve this problem, we can set up a system of two equations to represent the given information. By solving the system using the substitution method, we find that there are 8 nickels and 22 dimes.
Step-by-step explanation:
To solve this problem, we can set up a system of two equations.
Let x be the number of nickels and y be the number of dimes.
We can write the first equation as: x + y = 30, since there are 30 coins in total.
We can also write the second equation as: 0.05x + 0.10y = 2.60, since the value of the nickels (0.05x) plus the value of the dimes (0.10y) equals $2.60.
To solve the system, we can use the substitution or elimination method. I will solve it using the substitution method:
From the first equation, we can isolate x: x = 30 - y.
Substitute this value of x into the second equation: 0.05(30 - y) + 0.10y = 2.60.
Simplify and solve for y: 1.5 - 0.05y + 0.10y = 2.60. Combine like terms: 0.05y = 1.1. Divide both sides by 0.05: y = 22.
Now substitute the value of y back into the first equation to find x: x + 22 = 30. Subtract 22 from both sides: x = 8.
Therefore, there are 8 nickels and 22 dimes.