Question 476970
Let {{{j}}} = John's age now
Let {{{b}}} = Bob's age now
given:
(1) {{{ j - 1 = 2*( b - 1 ) }}}
(2) {{{ j + 7 = 1.5*( b + 7 ) }}}
Note that "half again" means 1.5 times
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(1) {{{ j - 1 = 2*( b - 1 ) }}}
(1) {{{ j - 1 = 2b - 2 }}}
(1) {{{ 2b - j = 1 }}}
and
(2) {{{ j + 7 = 1.5*( b + 7 ) }}}
(2) {{{ j + 7 = 1.5b + 10.5 }}}
(2) {{{ -1.5b + j = 3.5 }}}
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Add (1) and (2)
(1) {{{ 2b - j = 1 }}}
(2) {{{ -1.5b + j = 3.5 }}}
{{{ .5b = 4.5 }}}
{{{ b = 9 }}}
Plug this result back into (1)
(1) {{{ 2b - j = 1 }}}
(1) {{{ 2*9 - j = 1 }}}
(1) {{{ j = 18 - 1 }}}
(1) {{{ j = 17 }}}
John is 17 now and Bob is 9 now
check:
(2) {{{ j + 7 = 1.5*( b + 7 ) }}}
(2) {{{ 17 + 7 = 1.5*( 9 + 7 ) }}}
(2) {{{ 24 = 1.5*16 }}}
(2) {{{ 24 = 24 }}} 
OK