Question 600618
Let {{{ a }}} = number of 1's
Let {{{ b }}} = number of 5's
Let {{{ c }}} = number of 20's
given:
(1) {{{ c = a + b }}}
(2) {{{ a + b + c = 14 }}}
(3) {{{ 1a + 5b + 20c = 159 }}}
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Substitute (1) into (2) and
(1) into (3)
(2) {{{ a + b + a + b = 14 }}}
(2) {{{ 2a + 2b = 14 }}}
(2) {{{ a + b = 7 }}}
and
(3) {{{ 1a + 5b + 20*( a + b ) = 159 }}}
(3) {{{ 1a + 5b + 20a + 20b ) = 159 }}}
(3) {{{ 21a + 25b = 159 }}}
Multiply both sides of (2) by {{{ 21 }}}
and subtract (2) from (3)
(3) {{{ 21a + 25b = 159 }}}
(2) {{{ -21a - 21b = 147 }}}
{{{ 4b = 12 }}}
{{{ b = 3 }}}
and
(2) {{{ a + b = 7 }}}
(2) {{{ a + 3 = 7 }}}
(2) {{{ a = 4 }}}
and
(1) {{{ c = a + b }}}
(1) {{{ c = 4 + 3 }}}
(1) {{{ c = 7 }}}
She has 4 ones, 3 fives, and 7 twenties
check:
(3) {{{ 1a + 5b + 20c = 159 }}}
(3) {{{ 1*4 + 5*3 + 20*7 = 159 }}}
(3) {{{ 4 + 15 + 140 = 159 }}}
(3) {{{ 159 = 159 }}}
OK