Question 998423
{{{ n }}} = number of nickels
{{{ d }}} = number of dimes
{{{ q }}} = number of quarters
-------------------------
(1) {{{ n + d + q = 15 }}}
(2) {{{ 5n + 10d + 25q = 145 }}}
(3) {{{ q = (1/4)*( n + d ) }}}
-------------------------
(3) {{{ n + d = 4q }}}
Substitute this into (1) 
(1) {{{ 4q + q = 15 }}}
(1) {{{ 5q = 15 }}}
{{{ q = 3 }}}
---------------
Multiply both sides of (1) by {{{ 5 }}} 
and subtract (1) from (2)
(2) {{{ 5n + 10d + 25q = 145 }}}
(1) {{{ -5n - 5d - 5q = -75 }}}
--------------------------
{{{ 5d + 20q = 70 }}}
{{{ 5d + 20*3 = 70 }}}
{{{ 5d = 10 }}}
{{{ d = 2 }}}
-------------
(1) {{{ n + d + q = 15 }}}
(1) {{{ n + 2 + 3 = 15 }}}
(1) {{{ n = 10 }}}
--------------------
There are 10 nickels, 2 dimes, and 3 quarters
------------------------------------
check answers:
(2) {{{ 5n + 10d + 25q = 145 }}}
(2) {{{ 5*10 + 10*2 + 25*3 = 145 }}}
(2) {{{ 50 + 20 + 75 = 145 }}}
(2) {{{ 145 = 145 }}}
-----------------
(3) {{{ q = (1/4)*( n + d ) }}}
(3) {{{3 = (1/4)*( 10 +2 ) }}}
(3) {{{ 3 = (1/4)*12 }}}
(3) {{{ 3 = 3 }}}
OK