Could someone please help me?
A set of five natural numbers has a mean, median and mode. The mean is 100. Two of the numbers are 19 and 96. If the median is two less than the mode, what is the value of the mode?
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You have five natural numbers that sum to 500:
a + b + c + d + e = 500
You're told two are 19 and 96, leaving c, d and e, say:
19 + 96 + c + d + e = 500
The median, c, say, is two less than the mode:
c = d - 2 = e - 2
e and d will be the mode (i.e. d = e) since 19, 96 and c will be three distinct numbers and the mode is the score with the highest frequency (the other scores have frequency 1, and since there are only two numbers left, these two scores (i.e. frequency two) must be the mode).
So we have,
19 + 96 + c + d + e = 19 + 96 + (d-2) + d + d = 19 + 96 + 3d - 2 = 500
3d = 387, which means
d = 129.
Since d was one of the scores that comprised the mode, the mode is 129.
To check, the scores are:
19, 96, 127, 129, 129
They sum to 500, 127 is indeed the median, 129 the mode.
A stupid question I'm sure, but how did you know the sum was 500?