Question 918403
Let {{{ d }}} = number of dimes
Let {{{ q }}} = number of quarters
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(1) {{{ d + q = 60 }}}
(2) {{{ 10d + 25q = 1140 }}} ( in cents )
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(2) {{{ 2d + 5q = 228 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2d + 5q = 228 }}} 
(1) {{{ -2d - 2q = -120 }}}
{{{ 3q = 108 }}}
{{{ q = 36 }}}
and
(1) {{{ d + q = 60 }}}
(1) {{{ d = 60 - 36 }}}
(1) {{{ d = 24 }}}
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There are 24 dimes and 36 quarters
check:
(2) {{{ 10d + 25q = 1140 }}} 
(2) {{{ 10*24 + 25*36 = 1140 }}} 
(2) {{{ 240 + 900 = 1140 }}}
(2) {{{ 1140 = 1140 }}}
OK