Question 888195
Let {{{ a }}} = number of dollar coins
Let {{{ b }}} = number of quarters
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(1) {{{ a + b = 19 }}}
(2) {{{ 100a + 25b = 2000 - 925 }}} ( in cents )
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(2) {{{ 100a + 25b = 1075 }}}
Multiply both sides of (1) by {{{ 25 }}}
and subtract (1) from (2)
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(2) {{{ 100a + 25b = 1075 }}}
(1) {{{ -25a - 25b = -475 }}}
{{{ 75a = 600 }}}
{{{ a = 8 }}}
and, since,
(1) {{{ a + b = 19 }}}
(1) {{{ b = 11 }}}
There are 8 dollar coins
There are 11 quarters
check:
(2) {{{ 100*8 + 25*11 = 2000 - 925 }}} 
(2) {{{ 800 + 275 = 1075 }}}
(2) {{{ 1075 = 1075 }}}
OK