Sam ranks movies on a scale of 1-100. If he adds 2 points to each movie in his collection, and the range of the ranking was 54, what is the range when the 2 points are added ?
The same. High minus low still the same.
Well, if Sam adds 2 points to each movie in his collection, it's like giving them a little boost, a mini make-over, if you will. As for the range, it's the difference between the highest and lowest ranking. So, if the original range was 54, and he added 2 points to each movie, it's like stretching out a rubber band just a little bit. The range will increase by 2, my friend! So, the range when the 2 points are added is 56.
To find the new range when 2 points are added to each movie in Sam's collection, we need to consider the original range and add 2 to both the upper and lower limits.
Given that the original range is 54, we can divide it into two parts: the upper limit and the lower limit.
Let's assume the lower limit of the range is x.
So, the upper limit of the range would be x + 54.
Now, if Sam adds 2 points to each movie, the new lower limit would be x + 2, and the new upper limit would be (x + 54) + 2, which simplifies to x + 56.
The new range is determined by subtracting the new lower limit from the new upper limit:
New Range = (x + 56) - (x + 2)
= x + 56 - x - 2
= 54
Therefore, the range remains 54 when Sam adds 2 points to each movie in his collection.
To find the new range after adding 2 points to each movie ranking, we need to subtract the minimum ranking before adding 2 points from the maximum ranking before adding 2 points.
Let's say the original minimum ranking was m and the original maximum ranking was M.
After adding 2 points to each movie ranking, the new minimum ranking will be (m + 2) and the new maximum ranking will be (M + 2).
Therefore, the new range will be:
New Range = (new maximum ranking) - (new minimum ranking)
= (M + 2) - (m + 2)
= M - m
Since we know the original range was 54, we have:
54 = M - m
Solving for M - m:
M - m = 54
So, the new range when 2 points are added to each movie ranking is 54.