Question

4 numbers are displayed in a row. The average of the first two numbers is 8, the average of the 2nd and 3rd number is 9 and the average of the 3rd and4th number is 12.Find the average of the 1st and 4th number.

Answer 1

11

Explanation:

Let the four numbers be a, b, c, and d.

The average of the first two numbers is 8.

`(a+b)/(2)=8\implies a+b=16\cdots(1)`

The average of the 2nd and 3rd numbers is 9.

`(b+c)/(2)=9\implies b+c=18\cdots(2)`

The average of the 3rd and 4th numbers is 12.

`(c+d)/(2)=12\implies c+d=24\cdots(3)`

We want to find the average of the 1st and 4th numbers, a and d.

From equations 1 and 3:

`\begin{gathered} a+b=16 \\ c+d=24 \end{gathered}`

Add the two equations:

`a+b+c+d=40\cdots(4)`

Using equation (2): substitute 18 for b+c in equation 4:

`\begin{gathered} a+18+d=40 \\ a+d=40-18 \\ a+d=22 \\ \text{ Divide both sides by 2} \\ (a+d)/(2)=11 \end{gathered}`

The average of the 1st and fourth numbers is 11.