Question 766473
Let {{{ d }}} = number of dimes
Let {{{ q }}} = number of quarters
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(1) {{{ d + q = 21 }}}
(2) {{{ 10d + 25q = 390 }}} ( in cents )
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Multiply both sides of (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 10d + 25q = 390 }}}
(1) {{{ -10d - 10q = -210 }}}
{{{ 15q = 180 }}}
{{{ q = 12 }}}
and, since
(1) {{{ d + q = 21 }}}
(1) {{{ d + 12 = 21 }}}
(1) {{{ d = 9 }}}
He has 9 dimes and 12 quarters
check:
(2) {{{ 10*9 + 25*12 = 390 }}} 
(2) {{{ 90 + 300 = 390 }}}
(2) {{{ 390 = 390 }}}
OK