Question 703362
Let {{{ q }}} = number of quarters
Let {{{ d }}} = number of dimes
given:
(1) {{{ q + d = 38 }}}
(2) {{{ 25*(2q) + 10d = 1100 }}} ( in cents )
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(2) {{{ 50q + 10d = 1100 }}}
(2) {{{ 5q + d = 110 }}}
Subtract (1) from (2)
(2) {{{ 5q + d = 110 }}}
(1) {{{ -q - d = -38 }}}
{{{ 4q = 72 }}}
{{{ q = 18 }}}
and, since
(1) {{{ q + d = 38 }}}
(1) {{{ 18 + d = 38 }}}
(1) {{{ d = 20 }}}
He has 18 quarters and 20 dimes
check:
(2) {{{ 50q + 10d = 1100 }}}
(2) {{{ 50*18 + 10*20 = 1100 }}}
(2) {{{ 900 + 200 = 1100 }}}
(2) {{{ 1100 = 1100 }}}
OK