Question 978407
At present:
(1) {{{ L/B = 1/2 }}}
In 3 years:
(2) {{{ ( L + 3 ) / ( B + 3 ) = 3/5 }}}
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(1) {{{ B = 2L }}}
By substitution:
(2) {{{ ( L + 3 ) / ( 2L + 3 ) = 3/5 }}}
Multiply both sides by {{{ 5*( 2L + 3 ) }}}
(2) {{{ 5*( L + 3 ) = 3*( 2L + 3 ) }}}
(2) {{{ 5L + 15 = 6L + 9 }}}
(2) {{{ L = 15 - 9 }}}
(2) {{{ L = 6 }}}
and, since
(1) {{{ B = 2L }}}
(1) {{{ B = 2*6 }}}
(1) {{{ B = 12 }}}
Lewis is 6 and Brown is 12
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check:
(2) {{{ ( L + 3 ) / ( B + 3 ) = 3/5 }}}
(2) {{{ ( 6 + 3 ) / ( 12 + 3 ) = 3/5 }}}
(2) {{{ 9/15 = 3/5 }}}
(2) {{{ ( 3/3 )*( 3/5 ) = 3/5 }}}
(2) {{{ 3/5 = 3/5 }}}
OK