Question 487951
Let {{{n}}} = number of nickels
Let {{{d}}} = number of dimes
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given:
(1) {{{ n + d = 48 }}}
(2) {{{ 5n + 10d = 450 }}}
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Multiply both sides of (1) by {{{5}}}
and subtract (1) from (2)
(2) {{{ 5n + 10d = 450 }}}
(1) {{{ -5n - 5d = -240 }}}
{{{ 5d = 210 }}}
{{{ d = 42 }}}
and, since
(1) {{{ n + d = 48 }}}
(1) {{{ n + 42 = 48 }}}
(1) {{{ n = 48 - 42 }}}
(1) {{{ n = 6  }}}
There are 6 nickels and 42 dimes in the jar
check:
(2) {{{ 5n + 10d = 450 }}}
(2) {{{ 5*6 + 10*42 = 450 }}}
(2) {{{ 30 + 420 = 450 }}}
(2) {{{ 450 = 450 }}}
OK