Question 772280
Let {{{ b }}} = Ben's age now
Let {{{ k }}} = Kris's age now
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(1) {{{ b - 5 = (2/3)*( k - 5 ) }}}
(2) {{{ b + 10 = (5/6)*( k + 10 ) }}}
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(1) {{{ 3*( b - 5 ) = 2*( k - 5 ) }}}
(1) {{{ 3b - 15 = 2k - 10 }}}
(1) {{{ 3b - 2k = 5 }}}
and
(2) {{{ 6*( b + 10 ) = 5*( k + 10 ) }}}
(2) {{{ 6b + 60 = 5k + 50 }}}
(2) {{{ 6b - 5k = -10 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and subtract (2) from (1)
(1) {{{ 6b - 4k = 10 }}}
(2) {{{ -6b + 5k = 10 }}}
{{{ k = 20 }}}
and, since
(1) {{{ 3b - 2k = 5 }}}
(1) {{{ 3b - 2*20 = 5 }}}
(1) {{{ 3b = 45 }}}
(1) {{{ b = 15 }}}
Ben is 15 and Kris is 20
check:
(1) {{{ b - 5 = (2/3)*( k - 5 ) }}}
(1) {{{ 15 - 5 = (2/3)*( 20 - 5 ) }}}
(1) {{{ 10 = (2/3)*15 }}}
(1) {{{ 30 = 2*15 }}}
(1) {{{ 30 = 30 }}}
OK -you can check other equation