I have $0.39. There is 1 more penny than nickel, and one more nickel than dimes. The coins are?
To determine the types of coins you have, let's break down the information given.
1. There is 1 more penny than nickel.
2. There is one more nickel than dimes.
3. The total value of the coins is $0.39.
Let's assign variables to represent the number of each type of coin. Let's assume the number of dimes is D, the number of nickels is N, and the number of pennies is P.
Based on the information given, we can form equations:
1. There is 1 more penny than nickel: P = N + 1
2. There is one more nickel than dimes: N = D + 1
3. The total value of the coins is $0.39: 0.01P + 0.05N + 0.10D = 0.39
Now let's solve the equations to find the values of P, N, and D.
From equation 1, we can substitute N in terms of D: P = (D + 1) + 1 = D + 2.
Now substitute P and N into equation 3 and solve for D:
0.01(D + 2) + 0.05(D + 1) + 0.10D = 0.39
0.01D + 0.02 + 0.05D + 0.05 + 0.10D = 0.39
0.16D + 0.07 = 0.39
0.16D = 0.39 - 0.07
0.16D = 0.32
D = 0.32 / 0.16
D = 2
Now that we know D = 2, we can substitute this value back into equation 2 to find N:
N = D + 1 = 2 + 1 = 3
And finally, substitute D and N into equation 1 to find P:
P = N + 1 = 3 + 1 = 4
Therefore, you have 4 pennies, 3 nickels, and 2 dimes.
4 pennies
3 nickels
2 dimes
Does that work?