Question 885519
Let {{{ m }}} = the man's age now
Let {{{ s }}} = his sister's age now
Let {{{ u }}} = uncles age now
given:
(1) {{{ m = 2s }}}
(2) {{{ m = (1/2)*u }}}
(3) {{{ s + 50 = (1/2)*( u + 50 ) }}}
------------------------------
This is 3 equations and 3 unknowns
so it's solvable
(3) {{{ 2*( s + 50 ) = u + 50 }}}
(3) {{{ 2s + 100 = u + 50 }}}
(3) {{{ u = 2s + 50 }}}
-----------------------
Substitute (3) into (2)
(2) {{{ m = (1/2)*( 2s + 50 ) }}}
(2) {{{ 2m = 2s + 50 }}}
(2) {{{ m = s + 25 }}}
-------------------
Substitute (1) into (2)
(2) {{{ 2s = s + 25 }}}
(2) {{{ s = 25 }}}
----------------
(3) {{{ u = 2s + 50 }}}
(3) {{{ u = 2*25 + 50 }}}
(3) {{{ u = 100 }}}
---------------
(1) {{{ m = 2s }}}
(1) {{{ m = 50 }}}
----------------
The man is 50
His sister is 25
Their uncle is 100
-----------------
check:
(3) {{{ s + 50 = (1/2)*( u + 50 ) }}}
(3) {{{ 25 + 50 = (1/2)*( 100 + 50 ) }}}
(3) {{{ 75 = (1/2)*150 }}}
(3) {{{ 150 = 150 }}}
OK