Question 556071
Let {{{d}}} = number of dimes
Let {{{q}}} = number of quarters
given:
(1) {{{ d + q = 700 }}}
(2) {{{ 10d + 25q = 14500 }}} ( in cents )
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Multiply both sides of (1) by {{{10}}}
and subtract (1) from (2)
(2) {{{ 10d + 25q = 14500 }}}
(1) {{{ -10d - 10q = -7000 }}}
{{{ 15q = 7500 }}}
{{{ q = 500 }}}
and, since
(1) {{{ d + q = 700 }}}
(1) {{{ d + 500 = 700 }}}
(1) {{{ d = 200 }}}
There are 200 dimes and 500 quarters
check answer:
(2) {{{ 10d + 25q = 14500 }}}
(2) {{{ 10*200 + 25*500 = 14500 }}}
(2) {{{ 2000 + 12500 = 14500 }}}
(2) {{{ 14500 = 14500 }}}
OK