Question 849149
Wow! Wasn't that the cast of "Green Acres" ?
Let {{{ b }}} = the Boy's age now
Let {{{ y }}} = the young girl's age now
Let {{{ t }}} = Tony's age now
Let {{{ g }}} = Gary's age now
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(1) {{{ y = (1/3)*g }}}
(2) {{{ b = (1/4)*t }}}
(3) {{{ b + 4 = (1/4)*( g+4 ) }}}
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When the boy was born, the young girl was 
a quarter of the age of the butcher, Tony.
That means the difference in their ages,
(4) {{{ y - b = (1/4)*t }}}
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(2) {{{ t = 4b }}}
Substitute (2) into (4)
(4) {{{ y - b = (1/4)*4b }}}
(4) {{{ 4y - 4b = 4b }}}
(4) {{{ y - b = b }}}
(4) {{{ y = 2b }}}
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(1) {{{ g = 3y }}}
Substitute (1) into (3)
(3) {{{ b + 4 = (1/4)*( 3y+4 ) }}}
(3) {{{ 4b + 16 = 3y + 4 }}}
(3) {{{ 3y = 4b + 12 }}}
and, from (4),
(4) {{{ 3y = 6b }}}
By substitution:
{{{ 6b = 4b + 12 }}}
{{{ 2b = 12 }}}
{{{ b = 6 }}}
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(4) {{{ y = 2b }}}
(4) {{{ y = 12 }}}
and
(2) {{{ t = 4b }}}
(2) {{{ t = 4*6 }}}
(2) {{{ t = 24 }}}
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(1) {{{ g = 3y }}}
(1) {{{ g = 3*12 }}}
(1) {{{ g = 36 }}}
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The boy is 6
check:
(4) {{{ y - b = (1/4)*t }}}
(4) {{{ 12 - 6 = (1/4)*24 }}}
(4) {{{ 6 = 6 }}}
and
(3) {{{ b + 4 = (1/4)*( g+4 ) }}}
(3) {{{ 6 + 4 = (1/4)*( 36+4 ) }}}
(3) {{{ 10 = (1/4)*40 }}}
(3) {{{ 10 = 10 }}}
OK