Question 1091997
Let {{{ a }}} = Mary's age now
Let {{{ b }}} = Melinda's age now
Let {{{ c }}} = Monica's age now
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(1) {{{ ( a + b + c )/3 = 12 }}}
(2) {{{ a = b + 4 }}}
(3) {{{ c = (1/2)*a }}}
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There are 3 equations and 3 unknowns,
so it is solvable
(2) {{{ b = a - 4 }}}
Substitute (2) and (3) into (1)
(1) {{{ ( a + a - 4 + (1/2)*a ) / 3 = 12 }}}
(1) {{{ ( 5/2 )*a - 4  = 36 }}}
(1) {{{ 5a - 8 = 72 }}}
(1) {{{ 5a = 80 }}}
(1) {{{ a = 16 }}}
and
(2) {{{ b = a - 4 }}}
(2) {{{ b = 16 - 4 }}}
(2) {{{ b = 12 }}}
and
(3) {{{ c = (1/2)*a }}}
(3) {{{ c = (1/2)*16 }}}
(3) {{{ c = 8 }}}
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Mary is 16
Melinda is 12
Monica is 8
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check:
(1) {{{ ( a + b + c )/3 = 12 }}}
(1) {{{ ( 16 + 12 + 8 )/3  12 }}}
(1) {{{ 36/3 = 12 }}}
(1) {{{ 36 = 36 }}}
OK