Question 559533
Let {{{ g/b }}} = the original ratio of girls to boys
given:
(1) {{{ g/b = 6/7 }}}
(2) {{{ ( g + 117 )/b = 7/6 }}}
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(1) {{{ 7g = 6b }}}
(1) {{{ b = (7/6)*g }}}
and
(2) {{{ 6*( g + 117 ) = 7b }}}
(2) {{{ 6g + 702 = 7*(7/6)*g }}}
(2) {{{ 36g + 4212 = 49g }}}
(2) {{{ 13g = 4212 }}}
(2) {{{ g = 324 }}}
and
(1) {{{ b = (7/6)*g }}}
(1) {{{ b = (7/6)*324 }}}
(1) {{{ b = 378 }}}
There were {{{ 324 + 378 = 702 }}}
pupils in the cafe at first
check answer:
(2) {{{ ( g + 117 )/b = 7/6 }}}
(2) {{{ ( 324 + 117 )/378 = 7/6 }}}
(2) {{{ 441/378 = 7/6 }}}
(2) {{{ 441*6 = 7*378 }}}
(2) {{{ 2646 = 2646 }}}
OK