Question 1015115
Let {{{ a }}} = share for 1 man
Let {{{ b }}} = share for 1 woman
Let {{{ c }}} = share for 1 boy
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(1) {{{ 6a + 12b + 17c = 400 }}}
(2) {{{ 2a = 5c }}}
(3) {{{ 2b = 3c }}}
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(2) {{{ a = (5/2)*c }}}
(3) {{{ b = (3/2)*c }}}
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Substitute (2) and (3) into (1)
(1) {{{ 6a + 12b + 17c = 400 }}}
(1) {{{ 6*(5/2)*c + 12*(3/2)*c + 17c = 400 }}}
(1) {{{ 15c + 18c + 17c = 400 }}}
(1) {{{ 50c = 400 }}}
(1) {{{ c = 8 }}}
and
(2) {{{ a = (5/2)*c }}}
(2) {{{ a = (5/2)*8 }}}
(2) {{{ a = 20 }}}
and
(3) {{{ b = (3/2)*c }}}
(3) {{{ b = (3/2)*8 }}}
(3) {{{ b = 12 }}}
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1 man, 1 woman, and 1 boy will get:
{{{ 20 + 12 + 8 = 40 }}}
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check:
(1) {{{ 6a + 12b + 17c = 400 }}}
(1) {{{ 6*20 + 12*12 + 17*8 = 400 }}}
(1) {{{ 120 + 144 + 136 = 400 }}}
(1) {{{ 400 = 400 }}}
OK