Question

Out of 13 consecutive integers, the average of the first 7 is "x". What is the average of all the integers? ​

Answer 1

Answer:

Step-by-step explanation:

let the consecutive integers be a-6,a-5,a-4,a-3,a-2,a-1,a,a+1,a+2,a+3,a+4,a+5,a+6

so the average of the first x=(a-6 + a-5 + a-4 + a-3 + a-2 + a-1 +a) /7

so it becomes x=(7a-21)/7

we can write it as 7×(a-3)/7=a-3

so we get a=x+3

so rewriting all the integers in terms of x,it is

x-9,x-8,x-7,x-6,x-5,x-4,x-3,x-2,x-1,x,x+1,x+2,x+3

finding the average of these we get (13x-39)/13=13×(x-3)/13= x-3

so the average of all the integers is x-3

i know that the answer has become too long

but i hope this helps you

thank you