Question 728956
Let {{{ x }}} = Bob's age now
Let {{{ y }}} = Ben's age now
{{{ x - 7 }}} = Bob's age 7 yrs ago
{{{ y - 7 }}} = Ben's age 7 yrs ago
{{{ x + 14 }}} = Bob's age in 14 yrs
{{{ y + 14 }}} = Ben's age in 14 yrs
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given:
(1) {{{ x - 7 = 2*( y - 7 ) }}}
(2) {{{ y + 14 = (4/5)*( x + 14 ) }}}
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(1) {{{ x - 7 = 2y - 14 }}}
(1) {{{ x - 2y = -7 }}}
and
(2) {{{ 5*( y + 14 ) = 4*( x + 14 ) }}}
(2) {{{ 5y + 70 = 4x + 56 }}}
(2) {{{ 4x - 5y = 14 }}}
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Multiply both sides of (1) by {{{ -4 }}}
and add the equations
(1) {{{ -4x + 8y = 28 }}}
(2) {{{ 4x - 5y = 14 }}}
{{{ 3y = 42 }}}
{{{ y = 14 }}}
and
(1) {{{ x - 2y = -7 }}}
(1) {{{ x - 2*14 = -7 }}}
(1) {{{ x = 28 - 7 }}}
(1) {{{ x = 21 }}}
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Bob is 21 and Ben is 14
check:
(2) {{{ y + 14 = (4/5)*( x + 14 ) }}}
(2) {{{ 14 + 14 = (4/5)*( 21 + 14 ) }}}
(2) {{{ 28 = (4/5)*35 }}}
(2) {{{ 28 = 28 }}}
and
(1) {{{ x - 7 = 2*( y - 7 ) }}}
(1) {{{ 21 - 7 = 2*( 14 - 7 ) }}}
(1) {{{ 14 = 2*7 }}}
(1) {{{ 14 = 14 }}}
OK