Question 1026149
Let {{{ b }}} = number of $1 bills
Let {{{ h }}} = number of half dollar coins
Let {{{ q }}} = number of quarters
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(1) {{{ q = 2h }}}
(2) {{{ h = b }}}
(3) {{{ 1*b + .5*h + .25q = 14 }}}
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(3) {{{ 100b + 50h + 25q = 1400 }}}
(3) {{{ 4b + 2h + q = 56 }}}
Substitute (1) and (2) into (3)
(3) {{{ 4*h + 2*h + 2*h = 56 }}}
(3) {{{ 8h = 56 }}}
(3) {{{ h = 7 }}}
and
(2) {{{ h = b }}}
(2) {{{ b = 7 }}}
and
(1) {{{ q = 2h }}}
(1) {{{ q = 2*7 }}}
(1) {{{ q = 14 }}}
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She has 
7 $1 bills
7 half dollar coins
14 quarters
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check:
(3) {{{ 1*b + .5*h + .25q = 14 }}}
(3) {{{ 1*7 + .5*7 + .25*14 = 14 }}}
(3) {{{ 7 + 3.5 + 3.5 = 14 }}}
(3) {{{ 14 = 14 }}}
OK