SOLUTION: So, I know this problem may seem really easy, but I'm a Elem. Ed major, and I'm taking this problem into a school to have children work through the problem, and I want to make sure

Question 400060: So, I know this problem may seem really easy, but I'm a Elem. Ed major, and I'm taking this problem into a school to have children work through the problem, and I want to make sure I'm not overlooking anything (occasionally happens) given the simplicity of the question.
Tom told his teacher that he would blow up the whole bag of balloons for the class party. He was faster and faster at blowing up balloons. It took Tom 20 second to blow up the first balloon in the bag. It took Tom 18 seconds to blow up the second balloon, 16 seconds to blow up the third balloon, and so on. It took Tom 4 seconds to blow up the last balloon in the bag. If Tom blew up all of the balloons, how many balloons were in the bag?
My answer is 9 ballons. I came up with it given the pattern that Tom was blowing the ballons up 20, 18, 16...4
Is there a way to do this algebraically? Thank you so much for your help.

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
this is an arithmetic series, with a difference of -2 (each term is 2 less than the preceding term)

any term can be described by ___ Tn = a + (n - 1)d
___ the nth term equals the 1st term (a) plus; the difference multiplied by, the number of the term minus one

to find the number of balloons (terms) ___ 4 = 20 + (n - 1)(-2)

-16 = (n - 1)(-2)

8 = n - 1 ___ 9 = n

hope this helps ... good luck with the kids
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