Question 1004818
Let {{{ a }}} = Albert's age now
{{{ a - 6 }}} = Albert's age 6 yrs ago
Let {{{ m }}} = his mother's age now
{{{ m - 6 }}} = his mother's age 6 yrs ago
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(1) {{{ a - 6 = (1/5)*( m - 6 ) }}}
(2) {{{ m = 3a }}}
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(2) {{{ a = m/3 }}}
Substitute (2) into (1)
(1) {{{ m/3 - 6 = (1/5)*( m - 6 ) }}}
(1) {{{ m - 18 = (3/5)*( m-6 ) }}}
(1) {{{ 5m - 90 = 3m - 18 }}}
(1) {{{ 2m = 72 }}}
(1) {{{ m = 36 }}}
His mother is 36
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check:
(2) {{{ a = m/3 }}}
(2) {{{ a = 36/3 }}}
(2) {{{ a = 12 }}}
and
(1) {{{ a - 6 = (1/5)*( m - 6 ) }}}
(1) {{{ a - 6 = (1/5)*(36 - 6 ) }}}
(1) {{{ a - 6 = (1/5)*30 }}}
(1) {{{ a - 6 = 6 }}}
(1) {{{ a = 12 }}}
OK