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