Question 777621
Let {{{ p }}} = Patrick's age now
Let {{{ a }}} = Alice's age now
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(1) {{{ p = a - 4 }}}
(2) {{{ p + 5 = (3/4)*( a + 5 ) }}}
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(2) {{{ 4*( p + 5 ) = 3*( a + 5 ) }}}
(2) {{{ 4p + 20 = 3a + 15 }}}
(2) {{{ 3a - 4p = 5 }}}
and
(1) {{{ p = a - 4 }}}
(1) {{{ a - p = 4 }}}
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Multiply both sides of (1) by {{{ 3 }}}
and subtract (2) from (1)
(1) {{{ 3a - 3p = 12 }}}
(2) {{{ -3a + 4p = -5 }}}
{{{ p = 7 }}}
and
(1) {{{ a - p = 4 }}}
(1) {{{ a - 7 = 4 }}}
(1) {{{ a = 11 }}}
Patrick is 7 now
check:
(2) {{{ p + 5 = (3/4)*( a + 5 ) }}}
(2) {{{ 7 + 5 = (3/4)*( 11 + 5 ) }}}
(2) {{{ 12 = (3/4)*16 }}}
(2) {{{ 4*12 = 3*16 }}}
(2) {{{ 48 = 48 }}}
OK