Question 916434
Let {{{ n }}} = the number of nickels in the box
Let {{{ d }}} = the number of dimes in the box
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(1) {{{ 5n + 10d = 1000 }}} ( in cents )
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Also given:
(2) {{{ 10n + 25d = 2125 }}}
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(1) {{{ n + 2d = 200 }}}
(2) {{{ 2n + 5d = 425 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2n + 5d = 425 }}}
(1) {{{ -2n - 4d = -400 }}}
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{{{ d = 25 }}}
and
(1) {{{ n + 2d = 200 }}}
(1) {{{ n + 2*25 = 200 }}}
(1) {{{ n = 200 - 50 }}}
(1) {{{ n = 150 }}}
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There are 150 nickels and 25 dimes in the box
check:
(1) {{{ 5*150 + 10*25 = 1000 }}} 
(1) {{{ 750 + 250 = 1000 }}}
(1) {{{ 1000 = 1000 }}}
and
(2) {{{ 10*150 + 25*25 = 2125 }}}
(2) {{{ 1500 + 625 = 2125 }}}
(2) {{{ 2125 = 2125 }}}
OK