Question 921649
Let {{{ a }}} = John's age now
Let {{{ b }}} = Jill's age now
Let {{{ c }}} = Jane's age now
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(1) {{{ a = 2c }}}
(2) {{{ a + 2 = 2*( b + 2 ) }}}
(3) {{{ b + 2 = 2*( c - 2 ) }}}
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(2) {{{ a + 2 = 2b + 4 }}}
(2) {{{ a - 2b = 2 }}}
and
(3) {{{ b + 2 = 2c - 4 }}}
(3) {{{ -b + 2c = 6 }}}
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(1) {{{ c = (1/2)*a }}}
Substitute (1) into (3)
(3) {{{ -b + 2c = 6 }}}
(3) {{{ 2*(1/2)*a - b = 6 }}}
(3) {{{ a - b = 6 }}}
Subtract (2) from (3)
(3) {{{ a - b = 6 }}}
(2) {{{ -a + 2b = -2 }}}
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{{{ b = 4 }}}
and
(3) {{{ a - b = 6 }}}
(3) {{{ a - 4 = 6 }}}
(3) {{{ a = 10 }}}
and
(1) {{{ c = (1/2)*a }}}
(1) {{{ c = 5 }}}
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John is 10
Jill is a 4
Jane is 5
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check:
John is twice Jane's age -OK
In 2 year’s time, john will be twice as old as jill
True- John will be 12 and Jill will be 6
Jill will be twice as old as jane’s age 2 years ago
True- Jane was 3 and Jill will be 6
OK