Question 1029418
Let {{{ a }}} = number of bologna sandwiches sold
Let {{{ b }}} = number of turkey sandwiches sold
Let {{{ c }}} = number of ham sandwiches sold
{{{ 30 }}} = number of roast beef sandwiches sold
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(1) {{{ a/b = 1/3 }}}
(2) {{{ b/c = 2/3 }}}
(3) {{{ a = (1/10)*( a + b + c + 30 ) }}}
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(3) {{{ 10a = a + b + c + 30 }}}
(3) {{{ 9a - b - c = 30 }}}
and
(1) {{{ a = (1/3)*b }}}
and
(2) {{{ c = (3/2)*b }}}
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By substitution:
(3) {{{ 9*(1/3)*b - b - (3/2)*b = 30 }}}
(3) {{{ 3b - b - (3/2)_*b = 30 }}}
(3) {{{ b*( 6/2 - 2/2 - 3/2 ) = 30 }}}
(3) {{{ b*( 1/2 ) = 30 }}}
(3) {{{ b = 60 }}}
and
(1) {{{ a = (1/3)*b }}}
(1) {{{ a = (1/3)*60 }}}
(1) {{{ a = 20 }}}
and
(2) {{{ c = (3/2)*b }}}
(2) {{{ c = (3/2)*60 }}}
(2) {{{ c = 90 }}}
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20 bologna sandwiches were sold
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check answer:
(3) {{{ a = (1/10)*( a + b + c + 30 ) }}}
(3) {{{ a = (1/10)*( 20 + 60 + 90 + 30 ) }}}
(3) {{{ a = 200/10 }}}
(3) {{{ a = 20 }}}
OK