Question 824483
Let {{{ m }}} = momma's age now
Let {{{ p }}} = papa's age now
Let {{{ t }}} = Tommy's age now
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(1) {{{ t + m + p = 70 }}}
(2) {{{ p = 6t }}}
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Let {{{ n }}} = the number of years
from now when the sum of their
ages will add up to {{{ 2*70 = 140 }}}
(3) {{{ t + n + m + n + p + n = 140 }}}
(3) {{{ t + m + p + 3n = 140 }}}
Substitute (1) into (3) 
(3) {{{ 70 + 3n = 140 }}}
(3) {{{ 3n = 70 }}}
(3) {{{ n = 70/3 }}}
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(4) {{{ t + 70/3 = (1/2)*( p + 70/3 ) }}}
(4) {{{ 2t + 140/3 = p + 70/3 }}}
(4) {{{ 6t + 140 = 3p + 70 }}}
(4) {{{ 3p = 6t + 70 }}}
Substitute (2) into (4)
(4) {{{ 3*(6t) = 6t + 70 }}}
(4) {{{ 18t = 6t + 70 }}}
(4) {{{ 12t = 70 }}}
(4) {{{ t = 5 + 10/12 }}}
Tommy is 5 yrs and 10 months
(2) {{{ p = 6t }}}
(2) {{{ p = 6*(70/12) }}}
(2) {{{ p = 35 }}}
Papa is 35
(1) {{{ t + m + p = 70 }}}
(1) {{{ 5 + 10/12 + 35 + m = 70 }}}
(1) {{{ m = 70 - 40 - 10/12 }}}
(1) {{{ m = 30 - 10/12 }}}
(1) {{{ m = 29 + 2/12 }}}
Momma is 29 and 2 months
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check:
(2) {{{ 6*( 5 + 10/12 ) = 30 + 5 }}}
(2) {{{ 30 + 5 = 35 }}}
(2) {{{ 35 = 35 }}}
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{{{ n = 70/3 }}}
{{{ n = 23 + 4/12 }}}
(3) {{{ t + m + p + 3n = 140 }}}
(3) {{{ 5 + 10/12 + 29 + 2/12 + 35 + 3*( 23 + 4/12 ) = 140 }}}
(3) {{{ 69 + 1 + 69 + 1 = 140 }}}
(3) {{{ 138 + 2 = 140 }}}
(3) {{{ 140 = 140 }}}
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(4) {{{ t + 70/3 = (1/2)*( p + 70/3 ) }}}
(4) {{{ 5 + 10/12 + 23 + 4/12 = (1/2)*( 35 + 23 + 4/12 ) }}}
(4) {{{ 29 + 2/12 = (1/2)*( 58 + 4/12 ) }}}
(4) {{{ 58 + 4/12 = 58 + 4/12 }}}
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(1) {{{ t + m + p = 70 }}}
(1) {{{ 5 + 10/12 + 29 + 2/12 + 35 = 70 }}}
(1) {{{ 34 + 1 + 35 = 70 }}}
(1) {{{ 70 = 70 }}}
OK
Hope I got it