Question 894900
Let the amounts paid by each = a, b, and c
given:
(1) {{{ a / ( b + c ) = 2/3 }}}
(2) {{{ b = .2*( a + c ) }}}
(3) {{{ c = b + 84 }}}
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This is 3 equations and 3 unknowns, so it's solvable
Multiply both sides of (1) by {{{ 3*( b + c ) }}}
(1) {{{ 3a = 2*( b + c ) }}}
(1) {{{ 3a = 2b + 2c }}}
and
(2) {{{ b = .2a + .2c }}}
(2) {{{ .2a = b - .2c }}}
(2) {{{ a = 5b - c }}}
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Substitute (2) into (1)
(1) {{{ 3*( 5b - c ) = 2b + 2c }}}
(1) {{{ 15b - 3c = 2b + 2c }}}
(1) {{{ 13b = 5c }}}
(1) {{{ b = ( 5/13 )*c }}}
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Substitute (1) into (3)
(3) {{{ c = b + 84 }}}
(3) {{{ c = (5/13)*c + 84 }}}
(3) {{{ 13c = 5c + 1092 }}}
(3) {{{ 8c = 1092 }}}
(3) {{{ c = 136.5 }}}
and
(3) {{{ c = b + 84 }}}
(3) {{{ b = c - 84 }}}
(3) {{{ b = 136.5 - 84 }}}
(3) {{{ b = 52.5 }}}
and
(1) {{{ a / ( b + c ) = 2/3 }}}
(1) {{{ a / ( 52.5 + 136.5 ) = 2/3 }}}
(1) {{{ a / 189 = 2/3 }}}
(1) {{{ 3a = 378 }}}
(1) {{{ a = 126 }}}
and
{{{ a + b + c = 126 + 52.5 + 136.5 }}}
{{{ a + b + c = 315 }}}
The present costs $315
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check:
(2) {{{ b = .2*( a + c ) }}}
(2) {{{ b = .2*( 126 + 136.5 ) }}}
(2) {{{ b = .2*262.5 }}}
(2) {{{ b = 52.5 }}}
OK
Hope I got it!