Question 548879
Let {{{n}}} = number of nickels
Let {{{q}}} = number of quarters
given:
(1) {{{ n + q = 23 }}}
(2) {{{ 5n + 25q = 235 }}} ( in cents )
----------------
Multiply both sides of (1) by 5 and subtract (1) from (2)
(2) {{{ 5n + 25q = 235 }}}
(1) {{{ -5n - 5q = -115 }}}
{{{ 20q = 120 }}}
{{{ q = 6 }}}
and, since
(1) {{{ n + 6 = 23 }}}
(1) {{{ n = 17 }}}
There are 17 nickels and 6 quarters
check:
(2) {{{ 5*17 + 25*6 = 235 }}}
(2) {{{ 85 + 150 = 235 }}}
(2) {{{ 235 = 235 }}}
OK