Question 564690
Let {{{d }}} = number of dimes
Let {{{ q }}} = number of quarters
given:
(1) {{{ d + q = 45 }}}
(2) {{{ 10d + 25q = 765 }}} ( in cents )
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(2) {{{ 2d + 5q = 153 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2d + 5q = 153 }}}
(1) {{{ -2d - 2q = -90 }}}
{{{ 3q = 63 }}}
{{{ q = 21 }}}
and, since
(1) {{{ d + 21 = 45 }}}
(1) {{{ d = 45 - 21 }}}
(1) {{{ d = 24 }}}
She has 24 dimes and 21 quarters
check:
(2) {{{ 10*24 + 25*21 = 765 }}}
(2) {{{ 240 + 525 = 765 }}}
(2) {{{ 765 = 765 }}}
OK