Question 129733
All of these type problems can be solved this way:
Let {{{a}}} = Alberto's age now
Let {{{r}}} = Rosa's age now
In order to talk about their ages 15 years ago,
you have to subtract 15 from EACH of their ages
{{{a - 15 = 2(r - 15)}}}
The next part is very tricky, and I sort of
take it one or two words at a time
It's about Alberto in 9 more years. That's
{{{a + 9}}}
He's going to be twice as old as something, so
I've got {{{a + 9}}}= 2 x ?
Now I've got the brain-twister
"twice as old as she was when he was as old as she is now."
I can grapple with it better if I put actual numbers on their
ages, just for now.
Say he is 10 and she is 6 now
4 years ago he was 6 like she is now. Call this age {{{a[2]}}}
{{{a[2] = a - (a-r)}}}
{{{a[2] = r}}}
because {{{r}}} is her age now, or 6 years old
This is "when he was as old as she is now."
Now how old was she?
{{{r[2] = r - (a - r)}}}
{{{r[2] = 2r - a}}}
This is "as old as she was", or {{{2*6 - 10 = 2}}}
Now I put it all together
{{{a + 9 = 2(2r - a)}}}
{{{a + 9 = 4r - 2a}}}
(1) {{{4r - 3a = 9}}}
and from above,
{{{a - 15 = 2(r - 15)}}}
{{{a - 15 = 2r - 30}}}
(2){{{2r - a = 15}}}
multiply (2) by {{{2}}} and subtract from (1)
{{{4r - 3a = 9}}}
{{{-4r + 2a = -30}}}
{{{-a = -21}}}
{{{a = 21}}} Alberto's age now
{{{4r - 3*21 = 9}}}
{{{4r = 63 + 9}}}
{{{4r = 72}}}
{{{r = 18}}} Rosa's age now
check answers
{{{a - 15 = 2(r - 15)}}}
{{{21 - 15 = 2(18 - 15)}}}
{{{6 = 2*3}}}
{{{6 = 6}}}
OK
{{{a + 9 = 2(2r - a)}}}
{{{21 + 9 = 2(2*18 - 21)}}}
{{{30 = 2(36 - 21)}}}
{{{30 = 2*15}}}
{{{30 = 30}}}
OK
whew!