This problem can be solved using a system of equations. Let x be the number of nickels and y be the number of dimes. We know that the total number of coins is 23, so we can write the first equation:
x + y = 23
We also know that the total value of the coins is $2.20. Since nickels are worth $0.05 and dimes are worth $0.10, we can write the second equation:
0.05x + 0.1y = 2.2
Now we have a system of two equations with two variables. To solve for x and y, we can use substitution or elimination method.
Substitution method:
We can solve for one variable in one equation, and substitute it into the other equation.
From the first equation: x + y = 23
y = 23 - x
Substitute this into the second equation
0.05x + 0.1(23-x) = 2.2
0.05x + 2.3 - 0.1x = 2.2
-0.05x = -0.1
x = 2
So, Bob has 2 nickels in his pocket. We can substitute this value of x back into the first equation to find the number of dimes:
x + y = 23
2 + y = 23
y = 21
Bob has 21 dimes in his pocket.
Elimination method
We can multiply one equation by a constant so that when we add the two equations, one variable will cancel out.
x + y = 23
0.05x + 0.1y = 2.2
multiply the first equation by 5
5x + 5y = 115
add both equations
5x + 5y = 115
0.05x + 0.1y = 2.2
5x + 0.05x = 115+2.2
5.05x = 117.2
x = 23.2/5.05 = 2
So, Bob has 2 nickels in his pocket. We can substitute this value of x back into the first equation to find the number of dimes:
x + y = 23
2 + y = 23
y = 21
Bob has 21 dimes in his pocket.
Both methods give the same result, which is Bob has 2 nickels and 21 dimes in his pocket.