Shane has nickels,dimes,and quarters. He has a total of 17.65. He has 11 fewer quarters than nickels and 6 times as many dimes as quarters

Question

Please answer the following question that asks how many coins she has

Answer 1

Given the information in the problem we can set up equations and use substitution to figure out how may of each coin type Shane has.

If N = #nickels ($.05), D = #dimes ($.10), and Q = #quarters ($.25) then

The total money is added by:  .05N + .1D + .25Q = 17.65

We also know that Q = N-11 since there are ll fewer quarters than nickels

and 6Q = D since there are 6 times as many dimes as quarters

 

So the equations we have are:

 

.05N + .1D + .25Q = 17.65

Q = N-11

6Q = D ....   or  6(N-11) = D  .....  D = 6N-66

 

Use substitution to find the number of nickels we have

 

.05N + .1(6N-66) + .25(N-11) = 17.65

.05N + .6N - 6.6 + .25N - 2.75 = 17.65

.9N -9.35 = 17.65

.9N = 17.65 + 9.35

.9N = 27

N = 27/.9

N = 30

 

We have 30 nickels

Q = N -11 = 30 - 11 = 19 quarters

D = 6Q = 6(19) 114 dimes

 

CHECK: .05N + .1D + .25Q = 17.65

             .05(30) + .1(114) + .25(19) = 17.65

              1.5 + 11.4 + 4.75 = 17.65

              17.65 = 17.65

Since this works out correctly we see that our answer is correct