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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?

 Mar 17, 2018
 #1
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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.

 Mar 17, 2018
 #2
avatar+101055 
+1

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

 Mar 19, 2018

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