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/
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