Question 713889
Let {{{ n }}} = number of nickels
Let {{{ q }}} = number of quarters
given:
(1) {{{ n + q = 200 }}}
(2) {{{ 5n + 25q = 3000 }}} ( in cents )
----------------------
Multiply both sides of (1) by {{{ 5 }}}
and subtract (1) from (2)
(2) {{{ 5n + 25q = 3000 }}}
(1) {{{ -5n - 5q = -1000 }}}
{{{ 20q = 2000 }}}
{{{ q = 100 }}}
and, since
(1) {{{ n + q = 200 }}}
(1) {{{ n + 100 = 200 }}}
(1) {{{ n = 100 }}}
There are 100 quarters and 100 nickels
check:
(2) {{{ 5n + 25q = 3000 }}}
(2) {{{ 5*100 + 25*100 = 3000 }}}
(2) {{{ 500 + 2500 = 3000 }}}
(2) {{{ 3000 = 3000 }}}
OK