Question

The average of a set of four number is x, when a fifth number is added to the set, the average of the number is x+2. In terms of x, what is the number that was added

Answer 1

Hi,

Explanation:

Let's assume

`a_1,a_2,a_3,a_4\ the \ four\ numbers\\a_5\ the\ number\ added\\\\(a_1+a_2+a_3+a_4)/(4) =x\ \Longrightarrow\ a_1+a_2+a_3+a_4=4*x\\\\(a_1+a_2+a_3+a_4+a_5)/(5) =x+2\ \\\Longrightarrow\ (a_1+a_2+a_3+a_4)/(5)+(a_5)/(5) =x+2\\\Longrightarrow\ (4x)/(5)+ +(a_5)/(5) =x+2\\\\\Longrightarrow\ 4x+a_5=5x+10\\\\\Longrightarrow\ \boxed{a_5=x+10}\\`