SOLUTION: The arithmetic mean and median of five numbers a, a, b, c, c are 40 and 50 respectivly. If a < b < c , what is the value of a + c?

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Question 726525: The arithmetic mean and median of five numbers a, a, b, c, c are 40 and 50 respectivly. If a < b < c , what is the value of a + c?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The median is the number that is in the middle if you arrange the values in order. (If there is an even number of values you average the two in the middle).
It is a number such that half of the values are lesser or equal and the othe half are greater or equal.
In this case, you have 5 values, listed in order, and the middle one is b=50, the median.
The average (or arithmetic mean) is
%28a%2Ba%2Bb%2Bc%2Bc%29%2F5=40
so, multiplying both sides times 5, we get
2a%2Bb%2B2c=40%2A5 --> 2a%2Bb%2B2c=200
Substituting b=50,
2a%2B2c%2B50=200 --> 2a%2B2c=200-50 --> 2a%2B2c=150 --> 2%28a%2Bc%29=150 --> a%2Bc=150%2F2 --> highlight%28a%2Bc=75%29