Question 183213
Let {{{n}}}= the number of nickels he found
Let {{{d}}}= the number of dimes he found
Let {{{q}}}= the number of quarters he found
given:
(1) {{{d = n + 3}}} 
(2) {{{q = 2d}}}
(3) {{{5n + 10d + 25q = 505}}} (this is in pennies)
Substitute (1) and (2) in (3)
(3) {{{5n + 10d + 25q = 505}}}
(3) {{{5n + 10*(n + 3) + 25*2d = 505}}}
(3) {{{5n + 10n + 30 + 50d = 505}}}
(3) {{{15n + 50d = 475}}}
Substitute (1) in (3)
(3) {{{15n + 50*(n + 3) = 475}}}
(3) {{{15n + 50n + 150 = 475}}}
(3) {{{65n = 325}}}
(3) {{{n = 5}}}
Plug this back into (1)
(1) {{{d = n + 3}}} 
(1) {{{d = 5 + 3}}}
(1) {{{d = 8}}}
And from (2)
(2) {{{q = 2d}}}
(2) {{{q = 16}}}
Sam found 5 nickels, 8 dimes, and 16 quarters
check:
(1) {{{d = n + 3}}}
{{{8 = 5 + 3}}}
{{{8 = 8}}} 
(2) {{{q = 2d}}}
{{{16 = 2*8}}}
{{{16 = 16}}}
(3) {{{5n + 10d + 25q = 505}}}
{{{5*5 + 10*8 + 25*16 = 505}}}
{{{25 + 80 + 400 = 505}}}
{{{505 = 505}}}
OK