Question 720739
Let {{{ d }}} = number of dimes
Let {{{ q }}} = number of quarters
given:
(1) {{{ d + q = 110 }}}
(2) {{{ 10d + 25q = 2165 }}}
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Multiply both sides of (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 10d + 25q = 2165 }}}
(1) {{{ -10d - 10q = -1100 }}}
{{{ 15q = 1065 }}}
{{{ q = 71 }}}
and, since
(1) {{{ d + q = 110 }}}
(1) {{{ d + 71 = 110 }}}
(1) {{{ d = 39 }}}
The number of dimes is 39
The number of quarters is 71
check:
(2) {{{ 10*39 + 25*71 = 2165 }}}
(2) {{{ 390 + 1775 = 2165 }}}
(2) {{{ 2165 = 2165 }}}
OK