Question 529992
Let {{{a}}} = A's age now
Let {{{b}}} = B's age now
{{{ a - 7 }}} = A's age 7 years ago
{{{ b - 7 }}} = B's age 7 years ago
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given:
7 years ago, A was 3 years younger than B is now
(1) {{{ a - 7 = b - 3 }}}
7 years ago, B was twice as young as A ( half A's age )
(2) {{{ b - 7 = (1/2)*(a - 7) }}}
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(2) {{{ 2*(b - 7) = a - 7 }}}
(2) {{{ 2b - 14 = a - 7 }}}
(2) {{{ a - 2b = -7 }}}
and
(1) {{{ a - 7 = b - 3 }}}
(1) {{{ a - b = 4 }}}
(1) {{{ -b = -a + 4 }}}
(1) {{{ b = a - 4 }}}
Substitute (1) into (2)
(2) {{{ a -2*(a - 4) = -7 }}}
(2) {{{ a - 2a + 8 = -7 }}}
(2) {{{ -a = -15 }}}
(2) {{{ a = 15 }}}
A is 15
check:
(1) {{{ b = a - 4 }}}
(1) {{{ b = 15 - 4 }}}
(1) {{{ b = 11 }}}
(2) {{{ b - 7 = (1/2)*(a - 7) }}}
(2) {{{ 11 - 7 = (1/2)*(15 - 7) }}}
(2) {{{ 4 = (1/2)*8 }}}
(2) {{{ 4 = 4 }}}
OK