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Home Q & A Board Science-Related Homework Help Mathematics
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irina irina
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Posts: 919
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11 years ago
The median of a list of 97 consecutive integers is 55. What is the greatest integer in the list? Can someone please tell me the best way to solve this problem step by step?
Umm.. I still don't really understand... Why do you subtract one and divide that by 2?
Oh. Wait. I see. Thank you. I totally get it now.
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wrote...
#1
11 years ago
[n + (n+97-1)] / 2 = 55
2n + 96 = 110
n = 14 / 2 = 7

answer = n + 97 - 1 = 103
wrote...
#2
11 years ago
i believe the answer is 103
wrote...
#3
11 years ago
97 consecutive integers means that you have 97 numbers, each one being a whole number.  The median is 55, meaning that 55 is the number in the middle of the list.

97 - 1 = 96
96 / 2 = 47  // Those two steps tell us how far the highest integer is from 55.
47 + 55 = 102

The greatest integer is 102.
wrote...
#4
11 years ago
Really simple... the middle number (median) is 55.

That means you have 48 numbers smaller than 55 and 48 numbers larger than 55.  All together you have 97 numbers:
48 + 1 + 48 = 97

Since these are consecutive integers, the smallest one will be 48 numbers before the median and the largest one will be 48 numbers past the median...

55 - 48 = 7
55 + 48 = 103

Answer:
The numbers go from 7 to 103.  55 is the one in the middle.
103 is the largest.
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