Question 524061
Let {{{n}}} = number of nickels
Let {{{d}}} = number of dimes
given:
(1) {{{ q + d = 100 }}}
(2) {{{ 25q + 10d = 1975 }}} ( in cents )
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Multiply both sides of (1) by {{{10}}},
and subtract (1) from (2)
(2) {{{ 25q + 10d = 1975 }}}
(1) {{{ -10q - 10d = -1000 }}}
{{{ 15q = 975 }}}
{{{ q = 65 }}}
and, since
(1) {{{ q + d = 100 }}}
(1) {{{ 65 + d = 100 }}}
(1) {{{ d = 100 - 65 }}}
(1) {{{ d = 35 }}}
There are 35 dimes and 65 quarters
check:
(2) {{{ 25q + 10d = 1975 }}}
(2) {{{ 25*65 + 10*35 = 1975 }}}
(2) {{{ 1625 + 350  = 1975 }}}
(2) {{{ 1975 = 1975 }}}
OK