Question 570162
Let {{{ a }}} = Aaron's age now
Let {{{ b }}} = Baron's age now
{{{ a + 5 }}} = Aaron's age in 5 yrs
{{{ b + 5 }}} = Baron's age in 5 yrs
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given:
(1) {{{ a = b + 3 }}}
(2) {{{ a + 5 = ( b + 5) / 2 + 11 }}}
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(2) {{{ 2a + 10 = b + 5 + 22 }}}
(2) {{{ 2a - b = 5 + 22 - 10 }}}
(2) {{{ 2a - b = 17 }}}
and
(1) {{{ a = b + 3 }}}
(1) {{{ a - b = 3 }}}
Subtract (1) from (2)
(2) {{{ 2a - b = 17 }}}
(1) {{{ -a + b = -3 }}}
{{{ a = 14 }}}
and, since
(1) {{{ a = b + 3 }}}
(1) {{{ 14 = b + 3 }}}
(1) {{{ b = 14 - 3 }}}
(1) {{{ b = 11 }}}
Aaron is 14 and Baron is 11
check:
(2) {{{ a + 5 = ( b + 5) / 2 + 11 }}}
(2) {{{ 14 + 5 = ( 11 + 5) / 2 + 11 }}}
(2) {{{ 19 = 16/2 + 11 }}}
(2) {{{ 19 = 8 + 11 }}}
(2) {{{ 19 = 19 }}}
OK