Question 1013837
Let {{{ a }}} = Luis's age now
Let {{{ b }}} = Michael's age now
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(1) {{{ a = b - 8 }}}
(2) {{{ b - 2 = 5*( a - 2 ) }}}
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(2) {{{ b - 2 = 5a - 10 }}}
(2) {{{ 5a - b = 8 }}}
and
(1) {{{ -a + b = 8 }}}
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Add the equations
(2) {{{ 5a - b = 8 }}}
(1) {{{ -a + b = 8 }}}
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{{{ 4a = 16 }}}
{{{ a = 4 }}}
and
(1) {{{ a = b - 8 }}}
(1) {{{4 = b - 8 }}}
(1) {{{ b = 12 }}}
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Luis is 4 and Michael is 12
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check:
Luis is 8 years younger
OK
2 yrs ago, Michael was 10
2 yrs ago Luis was 2
So Michael was 5 times as old as Luis
OK