Question 1014295
Let {{{ a }}} = pounds of extra weight for
passenger paying $8
Let {{{ b }}} = pounds of extra weight for
passenger paying $2
Let {{{ c }}} = pounds of extra weight for
passenger paying $24
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{{{ 8/a }}} = cost/pound of extra weight
{{{ 2/b }}} = cost/pound of extra weight
{{{ 24/c }}} = cost/pound of extra weight
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(1) {{{ 190 - ( a + b ) = 2*( 190 - c ) }}} ( I plugged in real numbers and came up with this )
(2) {{{ 8/a  = 2/b }}}
(3) {{{ 2/b = 24/c }}}
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This is 3 equations and 3 unknowns, so it's solvable
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(1) {{{ 190 - a - b = 380 - 2c }}}
(1) {{{ -a - b + 2c = 190 }}}
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(2) {{{ 8b = 2a }}}
(2) {{{ a = 4b }}}
and
(3) {{{ 2c = 24b }}}
(3) {{{ c = 12b }}}
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Substitute (2) and (3) into (1)
(1) {{{ -a - b + 2c = 190 }}}
(1) {{{ -4b - b + 2*12b = 190 }}}
(1) {{{ 24b - 5b = 190 }}}
(1) {{{ 19b = 190 }}}
(1) {{{ b = 10 }}}
and
(2) {{{ a = 4b }}}
(2) {{{ a = 40 }}}
and
(3) {{{ c = 12b }}}
(3) {{{ c =120 }}}
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{{{ 8/a }}} = cost/pound of extra weight
{{{ 2/b }}} = cost/pound of extra weight
{{{ 24/c }}} = cost/pound of extra weight
{{{ 8/40 = 1/5 }}}
{{{ 2/10 = 1/5 }}}
{{{ 24/120 = 1/5 }}}
$.20 = cost/pound of extra weight
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{{{ 190 - c = 190 - 120 }}}
{{{ 190 - 120 = 70 }}}
Maximum weight allowed without penalty:
70 pounds
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check:
{{{ 70 + a = 70 + 40 = 110 }}}
and
{{{ 70 + b = 70 + 10 = 80 }}}
and
{{{ 110 + 80 = 190 }}}
OK
You might want another opinion on this
-I'm not 100% sure
-hope I got it!