Question 979809
Let {{{ d }}} = number of dimes
Let {{{ h }}} = number of half dollars
given:
(1) {{{ h = 4d - 12 }}}
(2) {{{ 10d + 50h = 450 }}}
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(2) {{{ d + 5h = 45 }}}
(2) {{{ d = -5h + 45 }}}
and
(1) {{{ h = 4d - 12 }}}
Substitute (2) into (1)
(1) {{{ h = 4*( -5h + 45 ) - 12 }}}
(1) {{{ h = -20h + 180 - 12 }}}
(1) {{{ 21h = 168 }}}
(1) {{{ h = 8 }}}
and
(1) {{{ h = 4d - 12 }}}
(1) {{{ 8 = 4d - 12 }}}
(1) {{{ 4d = 20 }}}
(1) {{{ d = 5 }}}
You have 5 dimes and 8 half dollars
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check:
(2) {{{ 10d + 50h = 450 }}}
(2) {{{ 10*5 + 50*8 = 450 }}}
(2) {{{ 50 + 400 = 450 }}}
(2) {{{ 450 = 450 }}}
OK