Question 697611
Let {{{ a }}} = Arthur's age now
Let {{{ b }}} = Carol's age now
given:
(1) {{{ a = b + 10 }}}
(2) {{{ a - 9 = 3*( b - 9 ) }}}
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(2) {{{ a - 9 = 3b - 27 }}}
(2) {{{ a - 3b = -18 }}}
and
(1) {{{ a - b = 10 }}}
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Subtract (2) from (1)
(1) {{{ a - b = 10 }}}
(2) {{{ -a + 3b = 18 }}}
{{{ 2b = 28 }}}
{{{ b = 14 }}}
and
(1) {{{ a = b + 10 }}}
(1) {{{ a = 14 + 10 }}}
(1) {{{ a = 24 }}}
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{{{ a + 4 = 28 }}}
{{{ b + 4 = 18 }}}
In 4 years Arthur will be 24
In 4 years Carol will be 18
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check:
(2) {{{ a - 9 = 3*( b - 9 ) }}}
(2) {{{ 24 - 9 = 3*( 14 - 9 ) }}}
(2) {{{ 15 = 3*5 }}}
(2) {{{ 15 = 15 }}}
OK