Question 1033494
Let {{{ a }}} = number of nuts Charlotte has initially
Let {{{ b }}} = number of nuts Lydia has initially
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(1) {{{ a/b = 6/7 }}}
(2) {{{ ( a - 36 ) / ( b + 36 ) = 9/17 }}}
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(1) {{{ a = (6/7)*b }}}
and
(2) {{{ a - 36 = (9/17)*( b + 36 ) }}}
Substitute (1) into (2)
(2) {{{ (6/7)*b - 36 = (9/17)*( b + 36 ) }}}
Multiply both sides by {{{ 17/9 }}}
(2) {{{ ( 34/21 )*b - 68 = b + 36 }}}
(2) {{{ ( 34/21 )*b - b = 104 }}}
(2) {{{ ( 13/21 )*b = 104 }}}
(2) {{{ b = ( 21/13 )*104 }}}
(2) {{{ b = 168 }}}
and
(1) {{{ a = (6/7)*b }}}
(1) {{{ a = (6/7)*168 }}}
(1) {{{ a = 144 }}}
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Lydia has 168 nuts at first
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check:
(1) {{{ a/b = 6/7 }}}
(1) {{{ 144/168 = 6/7 }}}
(1) {{{ .8571429 = .8571429 }}}
and
(2) {{{ ( a - 36 ) / ( b + 36 ) = 9/17 }}}
(2) {{{ ( 144 - 36 ) / ( 168 + 36 ) = 9/17 }}}
(2) {{{ 108 / 204 = 9/17 }}}
(2) {{{ 5294118 = .5294118 }}}
OK