Hot Air Balloons

Date: 12/25/96 at 18:02:05
From: Laura Klein
Subject: Probably algebra

The question on my homework was:

A hot air balloon covered 2100 miles in 7 days.  If it covered 50 
miles more each day than the day before, how many miles did it cover 
each day?  

I think I have the answer, but I'm not sure.  Would it be this?:

day 1: x
day 2: x + 50
day 3: x + 100
day 4: x + 150

and so on, until you get to day 7, which is x+300, then 
7+1050 = 2100-1050 = 1050.  

Then, 1050 divided by 7  is 150 so my answer is:

day 1 = 150 miles
day 2 = 200 miles
day 3 = 250 miles
day 4 = 300 miles
day 5 = 350 miles
day 6 = 400 miles
day 7 = 450 miles

Is this right?

Date: 12/25/96 at 23:34:24
From: Doctor Mike
Subject: Re: probably algebra

I assume that when you typed "7+1050 = 2100-1050 = 1050," you meant to 
type 7x+1050 instead. Also, when you use an "=" sign, you should be 
sure that the things on either side of it are really equal. That way 
people reading your solution will be less likely to get confused.  
  
Your approach to the problem is absolutely right on! The key step is 
to decide that "x" has to equal something specific, like distance 
covered in the first day, and logically continue from there. The only 
thing I would work on is clarity of your presentation of the solution.  
A few extra words will never hurt, and they usually are appreciated.
    
First you state the important relationship accurately as:
  
    7x + 1050 = 2100 
  
At this point you could say you will subtract 1050 from both sides of 
the equation, or write "- 1050" under each side of the equation to 
get:
  
    7x = 1050  
   
You certainly want to avoid writing down something like 
"7x + 1050 = 2100 - 1050 = 1050" because that simply is not true.  
Remember what I said above about being sure that the 2 things on 
either side of the "=" sign always have to be equal. I know you know 
that, and writing it this way is a short-cut, but don't do it.
   
Now, what really happens next is that you are dividing both sides of 
the equation by 7 to get x = 150. This point about doing exactly 
the same thing to two things that are equal (left side and right side) 
can be well understood by a younger kid, by your parent, by a teacher, 
or whoever. When you really understand math, you want to show it by 
being clear and convincing.   
   
One more thing I want to say to you about your answer. I am VERY 
pleased that you finished it! Some people would have just solved 
x = 150 and left it at that. You remembered what the problem asked 
for, and put the final answer in exactly that form. Paying attention 
to detail like that, plus your logical insight, will help you get 
ahead. Good luck, and thanks for writing.  

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/