Question 697276
Let {{{ f }}} = Father's age now
Let {{{ s }}} = Son's age now
{{{ f + 10 }}} = Father's age in 10 years
{{{ s + 10 }}} = Son's age in 10 years
given:
(1) {{{ f = 2s }}}
(2) {{{ f + 10 = (5/3)*( s + 10 ) }}}
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(2) {{{ f + 10 = (5/3)*s + 50/3 }}}
Substitute (1) into (2)
(2) {{{ 2s + 10 = (5/3)*s + 50/3 }}}
(2) {{{ 6s + 30 = 5s + 50 }}}
(2) {{{ s = 50 - 30 }}}
(2) {{{ s = 20 }}}
and, since,
(1) {{{ f = 2s }}}
(1) {{{ f = 2*20 }}}
(1) {{{ f = 40 }}}
The Father is 40 and
The Son is 20
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check:
(2) {{{ f + 10 = (5/3)*( s + 10 ) }}}
(2) {{{ 40 + 10 = (5/3)*( 20 + 10 ) }}}
(2) {{{ 50 = (5/3)*30 }}}
(2) {{{ 50 = 50 }}}
OK