Question 511352
Let {{{a}}} = Alvero's age now
Let {{{b}}}= Alyssa's age now
given:
(1) {{{ ( a + 5 ) / ( b + 5 ) = 3/5 }}}
(2) {{{ ( a + 10 ) / ( b + 10 ) = 2/3 }}}
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(1) {{{ 5*( a + 5 ) = 3*( b + 5 ) }}}
(1) {{{ 5a + 25 = 3b + 15 }}}
(1) {{{ 5a - 3b = -10 }}}
and
(2) {{{ 3*( a + 10 ) = 2*( b + 10 ) }}}
(2) {{{ 3a + 30 = 2b + 20 }}}
(2) {{{ 3a - 2b = -10 }}}
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Multiply both sides of (1) by {{{2}}} and
multiply both sides of (2) by {{{3}}}
Then subtract (2) from (1)
(1) {{{ 10a - 6b = -20 }}}
(2) {{{ -9a + 6b = 30 }}}
{{{ a = 10 }}}
and
(1) {{{ 5a - 3b = -10 }}}
(1) {{{ 5*10 - 3b = -10 }}}
(1) {{{ -3b = -10 - 50 }}}
(1) {{{ b = 20 }}}
The sum of their ages is 30
check answer:
(1) {{{ ( a + 5 ) / ( b + 5 ) = 3/5 }}}
(1) {{{ ( 10 + 5 ) / ( 20 + 5 ) = 3/5 }}}
(1) {{{ 15/25 = 3/5 }}}
(1) {{{ 3/5 = 3/5 }}}
OK
(2) {{{ ( a + 10 ) / ( b + 10 ) = 2/3 }}}
(2) {{{ ( 10 + 10 ) / ( 20 + 10 ) = 2/3 }}}
(2) {{{ 20/30 = 2/3 }}}
(2) {{{ 2/3 = 2/3 }}}
OK