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### Hot Air Balloons

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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?
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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

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.

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
ahead. Good luck, and thanks for writing.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Middle School Algebra
Middle School Word Problems

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