Question 648711
Let {{{ b }}} = number of boys in original group
Let {{{ g }}} = number of girls in original group
--------------
When 15 boys leave, you have 
{{{ b - 15 }}} boys and {{{ g }}} girls, and 
you are given that
(1) {{{ g = 2*( b - 15 ) }}}
-------------------
When 45 girls leave, you have
{{{ b - 15 }}} boys
{{{ g - 45 }}} girls
You are given that
(2) {{{ b - 15 = 5*( g - 45 ) }}}
--------------------------
(1) {{{ g = 2b - 30 }}}
(1) {{{ 2b - g = 30 }}}
and
(2) {{{ b - 15 = 5g - 225 }}}
(2) {{{ -b + 5g = 210 }}}
--------------------
Multiply both sides of (1) by {{{ 5 }}}
and add the equations
(1) {{{ 10b - 5g = 150 }}}
(2) {{{ -b + 5g = 210 }}}
{{{ 9b = 360 }}}
{{{ b = 40 }}}
There were 40 boys in the original group
check:
(1) {{{ g = 2b - 30 }}}
(1) {{{ g = 2*40 - 30 }}}
(1) {{{ g = 80 - 30 }}}
(1) {{{ g = 50 }}}
and
(2) {{{ b - 15 = 5*( g - 45 ) }}}
(2) {{{ 40 - 15 = 5*( g - 45 ) }}}
(2) {{{ 25 = 5g - 225 }}}
(2) {{{ 5g = 250 }}}
(2) {{{ g = 50 }}}
OK