Question 445512
Let {{{n}}} = number of nickels
Let {{{q}}} = number of quarters
given:
(1) {{{ n + q = 84 }}}
(2) {{{ 5n + 25q = 1560 }}} (in cents)
Multiply both sides of (1) by {{{5}}}
and subtract (1) from (2)
(2) {{{ 5n + 25q = 1560 }}}
(1) {{{ -5n - 5q = -420 }}}
{{{ 20q = 1140 }}}
{{{ q = 57 }}}
and, since
(1) {{{ n + 57 = 84 }}}
(1) {{{ n = 27 }}}
He has 27 nickels and 57 quarters
check answer:
(2) {{{ 5n + 25q = 1560 }}}
(2) {{{ 5*27 + 25*57 = 1560 }}}
{{{ 135 + 1425 = 1560 }}}
{{{ 1560 = 1560 }}}
OK