



You may
see problems that look like this: 





Joe has 4
dollars more than Fred. 


Between
them, they have 10 dollars. 


How much
does each have? 





Here's
how it works. 


We're
going to call the number of dollars one of them has X. 





Which
one. 





Well, you
could use either one, 


but
generally in the problem it says something like: 


"as
Fred" or "than Joe." 


That's
who gets to be X. 


In our
problem, it says "than Fred" 


So... 


Fred
(actually Fred's dollars) gets to be X.






The
problem also says: 


"Joe
has 4 dollars more than Fred." 


That
means: 


Joe has X
+ 4 dollars.






The
problem also says: 


"Between
them, they have 10 dollars." 


That
means: 





Joe's
dollars + Fred's dollars = 10 dollars






"Fred's
dollars" is X. 


"Joe's
dollars" is X + 4



So ... 


X + X + 4
= 10






and we've
done stuff like that before. 











We said
that X was Fred's dollars, 


and X + 4
was Joe's dollars, 


so ... 


Fred has 3
dollars.



Joe has 3 + 4 =
7 dollars.






Here's
another one. 





Example: 





Leslie,
Chris, and Shawn all collect dinosaur eggs. 





Leslie
has five times as many dinosaur eggs as Chris. 


Shawn has
one dinosaur egg less than Chris. 


Together,
they have 27 dinosaur eggs. 


How many
does each one have? 





OK, in
this one we have both "as Chris" AND "than
Chris" 


so ... 


Chris gets to be
X. 





OK, it's
actually Chris' dinosaur eggs 


that get
to be X. 





The
problem says: 


"Leslie
has five times as many dinosaur eggs as Chris" 


so ... 


Leslie has 5
times X (also known as 5X). 





The
problem also says: 


"Shawn
has one dinosaur egg less than Chris" 


so ... 


Shawn has X  1 





Together
they have: 


27 dinosaur eggs 





Chris'
dinosaur eggs + Leslie's dinosaur eggs + 


Shawn's
dinosaur eggs = 27 


so ... 








Chris was
X so 


Chris has
4 dinosaur eggs. 


Shawn has
X  1 so 


Shawn has
3 dinosaur eggs 


Leslie
has 5X so 


Leslie
has 20 dinosaur eggs. 





copyright 2005 Bruce Kirkpatrick 
