Question 499402
Let {{{d}}} = number of dimes
Let {{{n}}} = number of nickels
given:
(1) {{{ n = d + 8 }}}
(2) {{{ 5n + 10d = 205 }}} ( in cents )
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divide both sides of (2) by {{{5}}}
(2) {{{ n + 2d = 41 }}}
Substitute (1) into (2)
(2) {{{ d + 8 + 2d = 41 }}}
(2) {{{ 3d = 33 }}}
(2) {{{ d = 11 }}}
and, since
(1) {{{ n = d + 8 }}}
(1) {{{ n = 11 + 8 }}}
(1) {{{ n = 19 }}}
He has 19 nickels and 11 dimes
check:
(2) {{{ 5n + 10d = 205 }}}
(2) {{{ 5*19 + 10*11 = 205 }}}
(2) {{{ 95 + 110 = 205 }}}
(2) {{{ 205 = 205 }}}
OK