Question 149033
d=number of dimes
n=number of nickels
q=number of quarters
coefficient=value of the coin


d+n+q=17----------------------because there are 17 coins in all
10d+5n+25q=205----------------because the total value is 205 cents
d=q+4-------------------------because there are four more dimes than quarters


Solve for n in the first equation
n=17-d-q
plug in d
n=17-q-4-q or 13-2q


Plug both d and q in the second equation
10(q+4)+5(13-2q)+25q=205


Disitribute
10q+40+65-10q+25q=205


Combine like terms
25q+105=205


Subtract 105 from both sides
25q=100


Divide by 25
q=4


number of quarters= 4


d=q+4
d=4+4
d=8


number of dimes=8


d+n+q=17
8+n+4=17


Simplify
12+n=17


Subtract 12
n=5


number of nickels=5


So,
number of quarters= 4
number of dimes=8
number of nickels=5