Question 889855
Let {{{ a }}} = number of 10 cent coins she has
Let {{{ b }}} = number of 20 cent coins she has
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(1) {{{ 10a + 20b = 310 }}}
(2) {{{ a + b = 19 }}}
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Multiply both sides of (2) by {{{ 10 }}}
and subtract (2) from (1)
(1) {{{ 10a + 20b = 310 }}}
(2) {{{ -10a - 10b = -190 }}}
{{{ 10b = 120 }}}
{{{ b = 12 }}}
and, since
(2) {{{ a + 12 = 19 }}}
(2) {{{ a = 7 }}}
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She has 7 of the 10 cent coins
She has 12 of the 20 cent coins