Question 612339
Let {{{ j }}} = Jenny's age now
Let {{{ b }}} = Brother's age now
Given:
(1) {{{ j = b + 5 }}}
(2) {{{ ( j - 4 )*( b - 4 ) = b^2 - ( j + 37 ) }}}
(2) {{{ j*b - 4b - 4j + 16 = b^2 - j - 37 }}}
(2) {{{ j*b - 4b + 16 = b^2 + 3j - 37 }}}
(2) {{{ j*b + 16 = b^2 + 4b + 3j - 37 }}}
(2) {{{ j*b + 53 = b^2 + 4b + 3j }}}
Substitute (1) into (2)
(2) {{{ ( b + 5 )*b + 53 = b^2 + 4b + 3*( b + 5 ) }}}
(2) {{{ b^2 + 5b + 53 = b^2 + 4b + 3b + 15 }}}
(2) {{{ 7b - 5b = 53 - 15 }}}
(2) {{{ 2b = 38 }}}
(2) {{{ b = 19 }}}
and, since
(1) {{{ j = b + 5 }}}
(1) {{{ j = 19 + 5 }}}
(1) {{{ j = 24 }}}
Jenny is 24 and her Brother is 19
check:
(2) {{{ ( j - 4 )*( b - 4 ) = b^2 - ( j + 37 ) }}}
(2) {{{ ( 24 - 4 )*( 19 - 4 ) = 19^2 - ( 24 + 37 ) }}}
(2) {{{ 20*15 = 361 - 61 }}}
(2) {{{ 300 = 300 }}}
OK