1. If the average of three numbers is [tex][tex]$V$[/tex][/tex], and one of the numbers is [tex][tex]$Z$[/tex][/tex] and another is [tex][tex]$Y$[/tex][/tex], what is the remaining number?

A. [tex][tex]$Z + Y - V$[/tex][/tex]
B. [tex][tex]$Z + V - 3 \cdot Y$[/tex][/tex]
C. [tex][tex]$\frac{Z}{3} - V \cdot Y$[/tex][/tex]
D. [tex][tex]$3V - Z - Y$[/tex][/tex]
E. [tex][tex]$V - Z - Y$[/tex][/tex]



Answer :

To determine the value of the remaining number when we know the average of three numbers and know two of the numbers, follow these steps:

1. Understand the relationship between the average and the sum:
The average of three numbers (let's call them [tex]\(X\)[/tex], [tex]\(Y\)[/tex], and [tex]\(Z\)[/tex]) is given by:
[tex]\[ V = \frac{X + Y + Z}{3} \][/tex]

2. Express the sum in terms of the average:
To get the sum of the three numbers from the average, rearrange the formula:
[tex]\[ X + Y + Z = 3V \][/tex]

3. Solve for the remaining number [tex]\(X\)[/tex]:
We need to isolate [tex]\(X\)[/tex] (the unknown number). We already know [tex]\(Y\)[/tex] and [tex]\(Z\)[/tex], so rearrange the equation:
[tex]\[ X = 3V - Y - Z \][/tex]

Therefore, the remaining number is given by:
[tex]\[ X = 3V - Y - Z \][/tex]

So the correct choice from the given options is not directly listed, but the closest to this value based on the notation is:
[tex]\[ 3V - Y - Z \][/tex]

Since this exact option is not shown, none of the options A to E is correct.

Given the choices, the intended correct formula should be:
[tex]\[ X = 3V - Y - Z \][/tex]