Question 814647
Set p = number of pennies
    n = number of nickles
    d = number of dimes
p(1) + n(5) + d(10) = 47
that is, the number of pennies x 1 cent + number nickles x 5 cents
            + number of dimes x ten cents equals 47 cents
p = 4n
p + n + d = 17

Substituting 4n for p in the above
4n + n + d = 17
5n + d = 17
Subtract 5n from each side
    d = 17 - 5n
We will now substitute 4n for p and ( 17-5n ) for d in
the equation
p(1) + n(5) + d(10) = 47

4n(1) +n(5) + (17-5n)(10) = 47
  9n + 170 - 50n = 47
  -41n + 170 = 47
Subtract 170 from each side
  -41n = 47 - 170
  -41n = -123
Divide each side by -41
     n = 3
Since p = 4n
     p = 4(3)
     p = 12
Since p + n + d = 17
     12 + 3 + d = 17
     15 + d = 17
       d = 2
So we have 12 pennies, 3 nickles and 2 dimes
   12 + 3(5) + 2(10) ?= 47
   12 + 15 + 20 ?= 47
Looks like it checks out.