Question 475944
Let {{{a}}} = apprentices earnings
Let {{{j}}} = journeyman's earnings
Let {{{m}}} = master carpenter's earnings
given:
(1) {{{ a + j + m = 5100 }}}
(2) {{{ j = 3a }}}
(3) {{{ m = 1.5j }}}
This is 3 equations and 3 unknowns,
so it's solvable
-------------------
(2) {{{ j = 3a }}}
(2) {{{ a = j/3 }}}
Substitute (2) and (3) into (1)
(1) {{{ a + j + m = 5100 }}}
(1) {{{ j/3 + j + 1.5j = 5100 }}}
Multiply both sides by {{{3}}}
(1) {{{ j + 3j + 4.5j = 15300 }}}
(1) {{{ 8.5j = 15300 }}}
(1) {{{ j = 1800 }}}
and,
(2) {{{ a = j/3 }}}
(2) {{{ a = 600 }}}
and,
(3) {{{ m = 1.5j }}}
(3) {{{ m = 1.5*1800 }}}
(3) {{{ m = 2700 }}}
$600 = apprentices earnings
$1800 = journeyman's earnings
$2700 = master carpenter's earnings
check:
{{{ 600 + 1800 + 2700 = 5100 }}}
{{{ 5100 = 5100 }}}
OK