Question 1002647
Let {{{ b }}} = the number of boys
Let {{{ g }}} = the number of girls
---------------------------
(1) {{{ g/b = 5/6 }}}
(1) {{{ g = (5/6)*b }}}
and
(2) {{{ (5/6)*g + (3/4)*b = 390 }}}
multiply both sides by {{{ 12 }}}
(2) {{{ 10g + 9b = 4680 }}}
------------------------
By substitution:
(2) {{{ 10*(5/6)*b + 9b = 4680 }}}
Multiply both sides by {{{ 6 }}}
(2) {{{ 50b + 54b = 28080 }}}
(2) {{{ 104b = 28080 }}}
(2) {{{ b = 270 }}}
270 of the students were boys
and
(1) {{{ g = (5/6)*b }}}
(1) {{{ g = (5/6)*270 }}}
(1) {{{ g = 225 }}}
check:
(2) {{{ (5/6)*g + (3/4)*b = 390 }}}
(2) {{{ (5/6)*225 + (3/4)*270 = 390 }}}
Multiply both sides by {{{12}}}
(2) {{{ 10*225 + 9*270 = 4680 }}}
(2) {{{ 2250 + 2430 = 4680 }}}
(2) {{{ 4680 = 4680 }}}
OK