Question 439540
Let {{{n}}} = number of nickels he has
Let {{{d}}} = number of dimes he has
given:
(1) {{{ 5n + 10d = 565 }}} (in cents)
(2) {{{ 5*(n+8) + 10*(2d) = 1045 }}} (in cents)
-----------------------------
(2) {{{ 5n + 40 + 20d = 1045 }}}
(2) {{{ 5n + 20d = 1005 }}}
Subtract (1) from (2)
(2) {{{ 5n + 20d = 1005 }}}
(1) {{{ -5n - 10d = -565 }}}
{{{ 10d = 440 }}}
{{{ d = 44 }}}
and
(1) {{{ 5n + 10*44 = 565 }}}
(1) {{{ 5n = 565 - 440 }}}
(1) {{{ 5n = 125 }}}
{{{ n = 25 }}}
He has 44 dimes
check:
(2) {{{ 5*(25+8) + 10*(2*44) = 1045 }}}
{{{ 165 + 880 = 1045 }}}
{{{ 1045 = 1045 }}}
OK