Question 1059140
Let {{{ n }}} = number of nickels
Let {{{ q }}} = number of quarters
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(1) {{{ n + q = 51 }}}
(2) {{{ 5n + 25q = 735 }}} ( in cents )
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Multiply both sides of (1) by {{{ 5 }}}
and subtract (1) from (2)
(2) {{{ 5n + 25q = 735 }}} 
(1) {{{ -5n - 5q = -255 }}}
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{{{ 20q = 480 }}}
{{{ q = 24 }}}
and
(1) {{{ n + q = 51 }}}
(1) {{{ n + 24 = 51 }}}
(1) {{{ n = 27 }}}
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There are 27 nickels and 24 quarters
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check:
(2) {{{ 5n + 25q = 735 }}} 
(2) {{{ 5*27 + 25*24 = 735 }}} 
(2) {{{ 135 + 600 = 735 }}}
(2) {{{ 735 = 735 }}}
OK