hi, could you please explain to me the following problem and the reasoning behind the solution? thank you!

5 numbers have an average (arithmetic mean) of 124 and a median of 140. What is the max possible value of the lowest number?

(Doh)

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- Oct 9th 2007, 03:11 AMsimonearithmetics
hi, could you please explain to me the following problem and the reasoning behind the solution? thank you!

**5 numbers have an average (arithmetic mean) of 124 and a median of 140. What is the max possible value of the lowest number?**

(Doh) - Oct 9th 2007, 10:57 AMJhevon
are we dealing with integers here? otherwise, it would be kind of hard, i think

let's say we are dealing with integers:

we have 5 numbers of which the median is 140. so we have two numbers that are greater than or equal to 140 and two which are less than or equal to 140. the max of the lowest number occurs when the numbers that are greater than or equal to 140 are at their minimum (that is 140). in other words, 3 of our 5 numbers are 140. the lowest will be among the other two.

the average is 124, thus the sum of all the numbers is 620. subtract 3*140 and we are left with 200. we want to split this into two numbers, one of which is only slightly less than the other. if we are working with integers, this is simply 101 and 99. the lowest number can be a maximum of 99. otherwise it is equal to the second number and is hence not really the lowest.