Question 505755
I guess the question is " How old are they now?"
Let {{{a}}} = my age now
Let {{{b}}} = her age now
given:
The difference in their ages is always {{{ a - b }}}
When I was {{{b}}} years old, how old was she?
She was {{{ b - ( a - b )  = 2b - a }}} yrs old
Now I am twice this age, or {{{ 4b - 2a }}}, so
{{{ a = 4b - 2a }}}
(1) {{{ 3a = 4b }}}
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When she is {{{a}}} yrs old, I will be {{{ a + ( a - b ) = 2a - b }}}
The sum of our ages is {{{63}}}, so
{{{ a + 2a - b = 63 }}}
(2) {{{ 3a - b = 63 }}}
Substitute (1) into (2)
(2) {{{ 4b - b = 63 }}}
(2) {{{ 3b = 63 }}}
(2) {{{ b = 21 }}}
and, since
(1) {{{ 3a = 4b }}}
(1) {{{ a = 4*21/ 3}}}
(1) {{{ a = 28 }}}
I am 28 and she is 21
check answer:
When I was 21, she was 21 - (28 - 21) = 14
I am twice this age, or 28
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When she is as old as I am now, or 28,  that will be in 28 - 21 = 7 years
and I will be 28 + 7 = 35, and the sum of our ages will be 28 + 35 = 63
OK