Respuesta :

Statement:

The arithmetic mean of 3 and 3p+5 is 31.

To find out:

The value of p.

Solution:

  • We know

[tex]mean \: \: \: = \: \: \: \frac{sum \: \: \: of \: \: \: all \: \: \: the \: \: \: terms}{number \: \: \: of \: \: \: terms} [/tex]

  • Therefore,

[tex] \frac{3 + (3p + 5)}{2} = 31 \\ = > \frac{3p + 8}{2} = 31 \\ = > 3p + 8 = 31 \times 2 \\ = > 3p + 8 = 62 \\ = > 3p = 62 - 8 \\ = > 3p = 54 \\ = > p = \frac{54}{3} \\ = > p = 18[/tex]

Answer:

The value of p is 18.