SOLUTION: out of seven numbers, average of first six number is 40 and avarage of last six number is 35. the first number is 55. so, what is the difference between first and last number?

Question 794180: out of seven numbers, average of first six number is 40 and avarage of last six number is 35. the first number is 55. so, what is the difference between first and last number?

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let the seven numbers be represented by
(1) {a,b,c,d,e,f,g} and
let sum(b-f) be the sum of numbers b through f.
For the average of the first six we have
(2) (a + sum(b-f))/6 = 40 or
(3) (a + sum(b-f)) = 240
We are given that the first number, a, is 55, so we have
(4) sum(b-f)) = 240 - a or
(5) sum(b-f)) = 240 - 55 or
(6) sum(b-f)) = 185
Now for the average of the last six numbers we have
(7)(sum(b-f) + g)/6 = 35 or
(8)(sum(b-f) + g) = 210
Now use (6) in (8) to get
(9) 185 + g = 210 or
(10) g = 210 - 185 or
(11) g = 25
Answer: The first number is 55 and the last number is 25, giving an absolute difference of 30.
PS We have no idea what the five in between numbers are!
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