Question 265878
Harry is twice as old as Sally was at the time when he was as old as Sally is now. Harry's age + Sally's age = 56 years. how old are they?
<pre><font size = 4 color = "indigo"><b>

Let H = Harry's age now.
Let S = Sally's age now.
Let x = the number of years ago talked about in the problem

The hard part is analyzing this sentence:

<font color = "red">Harry is twice as old as Sally was 
at the time when he was as old as Sally is now.</font>

That's quite a mouthfull.  Break that sentence down into two parts:

<font color = "red">1.  Harry is twice as old as Sally was...</font>

and 

<font color = "red">2.  ...at the time when he was as old as Sally is now.</font>

To part 1 add the words "<font color = "red">x years ago</font>"

<font color = "red">1.  Harry is twice as old as Sally was x years ago.</font>

Change the words "<font color = "red">as old as Sally was x years ago</font>" to "<font color = "red">S-x</font>"

<font color = "red">1.  Harry is twice S-x.</font>

Now we can write the equation:

{{{H = 2(S - x)}}}

To part 2, which is

<font color = "red">2.  ...at the time when he was as old as Sally is now.</font>

change the words "<font color = "red">at the time when</font>" to "<font color = "red">x years ago</font>",
and change "<font color = "red">he</font>" to "<font color = "red">Harry</font>" 

<font color = "red">2. x years ago, Harry was as old as Sally is now.</font>

Change the words "<font color = "red">as old as Sally is now</font>" to "<font color = "red">S years old</font>"

<font color = "red">2. x years ago, Harry was S years old.</font>

So now we can write the equation

{{{H - x = S}}}

The last sentence

Harry's age + Sally's age = 56 years.

is easily changed to

{{{H + S = 56}}}.

So we have this system of three equations and 3 unknowns:

{{{system(
H = 2(S - x),
H - x = S,
H + S = 56)}}}

Rewrite the first equation
{{{H = 2(S - x)}}}
{{{H=2S-2x}}}
{{{H-2S+2x=0}}}

Rewrite the second equation
{{{H - x = S}}}
{{{H-S-x=0}}}

Now the system is

{{{system(
H -2S + 2x=0,
H - S -x=0,
H + S = 56)}}}

Can you solve that system of 3 equations in 3 unknowns?
If not post again asking how.

Answers:  H=32, S=24, x=8.

Checking: 

8 years ago Sally was 16, and Harry is now twice that, since he's 32.
8 years ago Harry was 24, which is how old Sally is now, since she's 24.

That checks.

Edwin</pre>