Question 1043064
Let {{{ b }}} = number of boys in the band
Let {{{ g }}} = number of girls in the band
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On monday:
(1) {{{ ( g - 30 ) / b = 2/5 }}}
On tuesday:
(2) {{{ ( g - 30 ) / ( b - 40 ) = 2/1 }}}
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There are 2 equations and 2 unknowns, so it's solvable
Multiply both sides of (1) by {{{ 5b }}}
(1) {{{ 5*( g - 30 ) = 2b }}}
(1) {{{ 5g - 150 = 2b }}}
(1) {{{ 5g - 2b = 150 }}}
and
Multiply both sides of (2) by {{{ b - 40 }}}
(2) {{{ g - 30 = 2*( b - 40 ) }}}
(2) {{{ g - 30 = 2b - 80 }}}
(2) {{{ -g + 2b = 50 }}}
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Add (1) and (2)
(2) {{{ -g + 2b = 50 }}}
(1) {{{ 5g - 2b = 150 }}}
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{{{ 4g = 200 }}}
{{{ g = 50 }}}
and
(2) {{{ -g + 2b = 50 }}}
(2) {{{ -50 + 2b = 50 }}}
(2) {{{ 2b = 100 }}}
(2) {{{ b = 50 }}}
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100 students ( 50 girls and 50 boys ) are in the band
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check:
(1) {{{ ( g - 30 ) / b = 2/5 }}}
(1) {{{ ( 50 - 30 ) / 50 = 2/5 }}}
(1) {{{ 20/50 = 2/5 }}}
OK
(2) {{{ ( g - 30 ) / ( b - 40 ) = 2/1 }}}
(2) {{{ ( 50 - 30 ) / ( 50 - 40 ) = 2/1 }}}
(2) {{{ 20 / 10 = 2/1 }}}
OK