Question 829677
Set n = no of nickles
    d = no of dimes
   q = no of quarters
n = q + 8
for the equation above solve for q.
subtract 8 from each side
n - 8 = q or
q = n - 8
d = 3n
We know that
(no of dimes)(0.10) + (no of nickles)(0.05) + (no of quarters)(0.25) = 7.00
d*(0.10) + n*(0.05) + q(0.25) = 7.00
usually written
0.10d + 0.05n + 0.25q = 7.00
Use the two equations q = n - 8 , d = 3n 
and substitute (n-8) for q , and (3n) for d
0.10(3n) + 0.05n + 0.25(n - 8) = 7.00
0.30n + 0.05n + 0.25n - 2.00 = 7.00
add 2.00 to each side
0.30n + 0.05n + 0.25n = 9.00
0.60n = 9.00
multiply each side by 100
60n = 900
divide each side by 60
n = 15
d = 3n = 3(15) = 45
q = n - 8 = 15 - 8 = 7
Let's check
15*(0.05) + 45(0.10) + 7(0.25) ?= 7.00
0.75 + 4.50 + 1.75 = 7.00 which checks out