Question 723727
Let {{{ n }}} = number of 5 cent coins
Let {{{ m }}} = number of 20 cent coins
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given:
(1) {{{ n + m = 33 }}}
(2) {{{ 5n + 20m = 375 }}} ( in cents )
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Multiply both sides of (1) by {{{ 5 }}}
and subtract (1) from (2)
(2) {{{ 5n + 20m = 375 }}}
(1) {{{ -5n - 5m = -165 }}}
{{{ 15m = 210 }}}
{{{ m = 14 }}}
and, since
(1) {{{ n + m = 33 }}}
(1) {{{ n + 14 = 33 }}}
(1) {{{ n = 19 }}}
19 = number of 5 cent coins
14 = number of 20 cent coins
check answer:
(2) {{{ 5n + 20m = 375 }}} 
(2) {{{ 5*19 + 20*14 = 375 }}} 
(2) {{{ 95 + 280 = 375 }}}
(2) {{{ 375 = 375 }}}
OK