Question 1078087
Let {{{ d }}} = number of dimes
Let {{{ q }}} = number of quarters
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(1) {{{ d + q = 100 }}}
(2) {{{ 10d + 25q = 1900 }}} ( in cents )
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(2) {{{ 2d + 5q = 380 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2d + 5q = 380 }}}
(1) {{{ -2d - 2q = -200 }}}
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{{{ 3q = 180 }}}
{{{ q = 60 }}}
and
(1) {{{ d + q = 100 }}}
(1) {{{ d + 60 = 100 }}}
(1) {{{ d = 40 }}}
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There are 40 dimes and 60 quarters
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check:
(2) {{{ 10d + 25q = 1900 }}} 
(2) {{{ 10*40 + 25*60 = 1900 }}} 
(2) {{{ 400 + 1500 = 1900 }}}
(2) {{{ 1900 = 1900 }}}
OK