Question 563244
Let {{{ b }}} = Bill's age now
Let {{{ t }}} = Ted's age now
given:
(1) {{{ b + t = 34 }}}
(2) {{{ 2*( b - 5 ) + 3*( t - 5 ) = 59 }}}
----------------------------
(2) {{{ 2b - 10 + 3t - 15 = 59 }}}
(2) {{{ 2b + 3t = 59 + 25 }}}
(2) {{{ 2b + 3t = 84 }}}
Multiply both sides of (1) by {{{2}}}, and
subtract (1) from (2)
(2) {{{ 2b + 3t = 84 }}}
(1) {{{ -2b - 2t = -68 }}}
{{{ t = 16  }}}
and
(1) {{{ b + t = 34 }}}
(1) {{{ b + 16 = 34 }}}
(1) {{{ b = 34 - 16 }}}
(1) {{{ b = 18 }}}
Bill is 18 and Ted is 16
check:
(2) {{{ 2*( b - 5 ) + 3*( t - 5 ) = 59 }}}
(2) {{{ 2*( 18 - 5 ) + 3*( 16 - 5 ) = 59 }}}
(2) {{{ 2*13 + 3*11 = 59 }}}
(2) {{{ 26 + 33 = 59 }}}
(2) {{{ 59 = 59 }}}