Question 739958
Let {{{ b }}} = Beth's age now
Let {{{ j }}} = Jay's age now
{{{ b + 4 }}} = Beth's age in {{{ 4 }}} years
{{{ j - 3 }}} = Jay's age 3 years ago
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given:
(1) {{{ b = j + 3 }}}
(2) {{{ ( b + 4 )*( j - 3 ) = 75 }}}
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Substitute (1) into (2)
(2) {{{ ( j + 3 + 4 )*( j - 3 ) = 75 }}}
(2) {{{ ( j + 7 )*( j - 3 ) = 75 }}}
(2) {{{ j^2 + 7j - 3j - 21 = 75 }}}
(2) {{{ j^2 + 4j - 96 = 0 }}}
By looking at this I can see:
(2) {{{ ( j + 12 )*( j - 8 ) = 0 }}}
{{{ j = 8 }}} ( ignore negative answer )
and, since,
(1) {{{ b = j + 3 }}}
(1) {{{ b = 11 }}}
Beth is 11 and Jay is 8
check:
(2) {{{ ( b + 4 )*( j - 3 ) = 75 }}}
(2) {{{ ( 11 + 4 )*( 8 - 3 ) = 75 }}}
(2) {{{ 15*5 = 75 }}}
(2) {{{ 75 = 75 }}}
OK