Question 810501
Let {{{ d }}} = numbe of dimes
Let {{{ q }}} = number of quarters
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(1) {{{ d + q = 28 }}}
(2) {{{ 10d + 25q = 505 }}} ( in cents )
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Multiply both sides o (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 10d + 25q = 505 }}} 
(1) {{{ -10d - 10q = -280 }}}
{{{ 15q = 225 }}}
{{{ q = 15 }}}
and, since
(1) {{{ d + q = 28 }}}
(1) {{{ d = 13 }}}
There are 13 dimes and 15 quarters
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check:
(2) {{{ 10d + 25q = 505 }}} 
(2) {{{ 10*13 + 25*15 = 505 }}} 
(2) {{{ 130 + 375 = 505 }}}
(2) {{{ 505 = 505 }}}
OK