Question 683734
Let {{{ d }}} = number of dimes he has
Let {{{ q }}} = number of quarters he has
given:
(1) {{{ d + q = 42 }}}
(2) {{{ 10d + 25q = 600 }}} ( in cents )
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Multiply both sides of (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 10d + 25q = 600 }}} 
(1) {{{ -10d - 10q = -420 }}}
{{{ 15q = 180 }}}
{{{ q = 12 }}}
and, since
(1) {{{ d + q = 42 }}}
(1) {{{ d + 12 = 42 }}}
(1) {{{ d = 30 }}}
he has 30 dimes and 12 quarters
check:
(2) {{{ 10d + 25q = 600 }}}
(2) {{{ 10*30 + 25*12 = 600 }}}
(2) {{{ 300 + 300 = 600 }}}
(2) {{{ 600 = 600 }}}
OK