Question 697589
Let William's height = {{{ w }}}
Let Timothy's height = {{{ t }}}
Let James' height = {{{ j }}}
given:
(1) {{{ w + t + j = 11.25 }}}
( note that 3" is 1/4 of a foot )
(2) {{{ w = t - 1 }}}
( 12" is 1 foot )
(3) {{{ t = j + .75 }}}
( 9" is 3/4 of 1 foot )
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This is 3 equations and 3 unknowns, so it's solvable
Substitute (2) into (1)
(1) {{{ w + t + j = 11.25 }}}
(1) {{{ t - 1 + t + j = 11.25 }}}
and
(3) {{{ t = j + .75 }}}
(2) {{{ j = t - .75 }}}
Substitute (2) into (1)
(1) {{{ t - 1 + t + t - .75 = 11.25 }}} ( all units are in feet )
(1) {{{ 3t - 1.75 = 11.25 }}}
(1) {{{ 3t = 13 }}}
(1) {{{ t = 13/3 }}}
and, since
(2) {{{ j = t - .75 }}}
(2) {{{ j = 13/3 - 3/4 }}}
(2) {{{ j = 52/12 - 9/12 }}}
(2) {{{ j = 43/12 }}}
and
(1) {{{ w + t + j = 11.25 }}}
(1) {{{ w + 13/3 + 43/12 = 11.25 }}}
(1) {{{ w + 52/12 + 43/12 = 45/4 }}}
(1) {{{ w + 95/12 = 135/12 }}}
(1) {{{ w = 40/12 }}}
(1) {{{ w = 10/3 }}}
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William is 10/3 ft, or 3 ft 4 in
Timothy is 13/3 ft, or 4 ft 4 in
James is 43/12 ft, or 3 ft 7 in
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Hope I got it