+174 Bob has 45 coins in her piggy bank. She has one fewer nickel than she has dimes, and one fewer quarter than three times the number of nickels. If Bob has only nickels, dimes, and quarters, how many nickels does she have?
If the number of dimes = D, then:
The number of nickels = D - 1, and:
The number of quarters= 3[D - 1] - 1
D + D - 1 + 3[D - 1] - 1 = 45, solve for D
D = 10 - number of dimes
10 - 1 = 9 - number of nickles
3 x 9 - 1 = 26 - number of quarters.
+118608 Bob has 45 coins in her piggy bank. She has one fewer nickel than she has dimes, and one fewer quarter than three times the number of nickels. If Bob has only nickels, dimes, and quarters, how many nickels does she have?
N=number of nickels
D=number of dimes
Q=number of quarters
N+D+Q = 45
N=D-1
Q=3N+1
= 3(D-1)-1
= 3D-3-1
= 3D - 4
so
N=D-1
Q=3D-4
D= D
D-1 + 3D - 4 + D = 45
5D - 5 = 45
5D = 50
D = 10
N = 10-1 = 9
She has 9 nickels
