Question 377710
Tom, Linda and Alex have $120 dollars. Alex has the third of what Tom has and Linda has twice as much as Alex. How much money, in dollars, does Linda have?
<pre>
This one almost sets itself up because the words correspond almost
exactly with the algebraic equation.  Just interpret "have" and "has"
as an equal sign "=", and "of" as "times" indicated by • , and "twice as much"
as "2 times" or " 2 • ".


[Tom], [Linda] [and] Alex [have] [$120 dollars]
  |       |      |    |     |          | 
  T   +   L      +    A     =         120   


[Alex] [has] [a third] [of] [what Tom has] 
   |     |       |      |        |
   A     =      1/3     •        T


[Linda] [has] [twice as much as] [Alex]
  |       |         |       |          |
  L       =         2       •         A

Put those three equations together and

{{{system(T+L+A=120,A=expr(1/3)*T,L=2*A)}}}

Can you solve that system of equations?  You can simplify the middle one by
multiplying both sides by 3 and having:

{{{system(T+L+A=120,3*A=T,L=2*A)}}}

Now substitute 3*A for T and 2*A for L in

 T  +  L  + A = 120
3*A + 2*A + A = 120
          6*A = 120
            A = 20

Then L = 2*A = 2*(20) = 40
and  T = 3*A = 3*(20) = 60

So Tom has $T or $60, Linda has $L or $40, and Alex had $20.

Alex has $20, which is a third of the $60 that Tom has, and since Linda has
$40, that is indeed twice as much as Alex had, only $20. The question asks: 
"How much money, in dollars, does Linda have?"

And of course the answer is $40.

Edwin</pre>