Question 630286
Let the 3 parts be a, b, and c
given:
(1) {{{ a + b + c = 150 }}}
(2) {{{ b = (5/6)*a }}}
(3) {{{ c = (4/5)*b }}}
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(2) {{{ a = (6/5)*b }}}
Substitute (2) and (3) into (1)
(1) {{{ (6/5)*b + b + (4/5)*b = 150 }}}
(1) {{{ b*( 6/5 + 5/5 + 4/5 ) = 150 }}}
Multiply both sides by {{{ 5 }}}
(1) {{{ b*( 6 + 5 + 4 ) = 750 }}}
(1) {{{ b = 750 / 15 }}}
(1) {{{ b = 50  }}}
and, since
(3) {{{ c = (4/5)*b }}}
(3) {{{ c = (4/5)*50 }}}
(3) {{{ c = 40 }}}
and
(2) {{{ a = (6/5)*b }}}
(2) {{{ a = (6/5)*50 }}}
(20 {{{ a = 60 }}}
The lengths are 60, 50, and 40