Conrad has a collection of three types of coins: nickels, dimes, and quarters. there are five more nickels than quarters but four times as many dimes as quarters. if the entire collection is worth $5.85,how many nickels, dimes, and quarters are there?

N=number of nickles
d=number of dimes
q=number of quarters
use cents for everything

total value=585
5n+10d+25q=585
divide everybody by 5 to simplify
n+2d+5q=117

we have

nicles are 5 more than quarters
n=5+q

4 times as many dimes as quarters
d=4 times q
d=4q

sub those in
5+q+2(4q)+5q=117
5+6q+8q=117
5+14q=117
minus 5
14q=112
q=8

sub back
n=5+q
n=5+8
n=13

d=4q
d=4(8)
d=32

13 nickles
32 dimes
8 quarters
divide both sides by 22