Out of seven numbers, average of first six number is 40 and average of last six number is 35. the ...
Out of seven numbers, average of first six number is 40 and average of last six number is 35. the first number is 55. What is the difference between first and last number?
Answer/Solution
30
Steps/Work
Let the seven numbers be represented by
{a,b,c,d,e,f,g}
let sum(b-f) be the sum of numbers b through f.
For the average of the first six we have
(a + sum(b-f))/6 = 40
(a + sum(b-f)) = 240
We are given that the first number, a, is 55, so we have
sum(b-f) = 240 - a
sum(b-f) = 240 - 55
sum(b-f) = 185
Now for the average of the last six numbers we have
(sum(b-f) + g)/6 = 35
(sum(b-f) + g) = 210
185 + g = 210
g = 210 - 185
g = 25
The first number is 55 and the last number is 25 so, their difference is 30.
Answer A
{a,b,c,d,e,f,g}
let sum(b-f) be the sum of numbers b through f.
For the average of the first six we have
(a + sum(b-f))/6 = 40
(a + sum(b-f)) = 240
We are given that the first number, a, is 55, so we have
sum(b-f) = 240 - a
sum(b-f) = 240 - 55
sum(b-f) = 185
Now for the average of the last six numbers we have
(sum(b-f) + g)/6 = 35
(sum(b-f) + g) = 210
185 + g = 210
g = 210 - 185
g = 25
The first number is 55 and the last number is 25 so, their difference is 30.
Answer A