Final answer:
Keith has 3 pennies.
Step-by-step explanation:
To solve this problem, we need to set up a system of equations to represent the given information. Let's start by defining the variables:
p = number of pennies
n = number of nickels
d = number of dimes
Since the total number of coins is 12, we can write the equation:
p + n + d = 12
Next, we know that the value of the coins is $0.60, so we can write the equation:
0.01p + 0.05n + 0.10d = 0.60
We also know that there is one fewer nickel than dimes, so we can write the equation:
n = d - 1
To solve this system of equations, we can use the substitution method. Start by solving the third equation for n:
n = d - 1
Substitute this expression for n in the first equation:
p + (d - 1) + d = 12
Simplify:
p + 2d - 1 = 12
Rearrange the equation:
p + 2d = 13
Now substitute this expression for p + 2d in the second equation:
0.01(p + 2d) + 0.05n + 0.10d = 0.60
Simplify:
0.01p + 0.02d + 0.05n + 0.10d = 0.60
Rearrange the equation:
0.01p + 0.10d + 0.05n = 0.60
Now substitute the expression for n in terms of d:
0.01p + 0.10d + 0.05(d - 1) = 0.60
Simplify and solve for p:
0.01p + 0.10d + 0.05d - 0.05 = 0.60
0.01p + 0.15d = 0.65
Rearrange the equation:
0.15d = 0.65 - 0.01p
0.15d = 0.64 - 0.01p
15d = 64 - p
Since p is the number of pennies, it must be a whole number. The only whole number solution to this equation is p = 3.
Therefore, Keith has 3 pennies.