Question

Of the five numbers, whose average is 60, the first is one-fourth of the sum of the last four. The first number
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Answer 1

Answer:

$\sf{The \ first \ term \ is \ 60.}$

Given:

$\textsf{The five numbers whose average is 60.}$

$\textsf{The first number is one forth the sum of the last four.}$

To find:

• $\textsf{The first number.}$

Solution:

$\sf{Let \ the \ sum \ of \ last \ four \ number \ be \ 4x.} \\ \\ \sf{First \ number = \dfrac{4x}{4}=x} \\ \\ \boxed{\sf{Average =\dfrac{Sum \ of \ observations}{Number \ of \ observations}}} \\ \\ \\ \sf{60=\dfrac{x+4x}{5}} \\ \\ \\ \sf{\therefore{60=\dfrac{5x}{5}}} \\ \\ \\ \boxed{\sf{\therefore{x=60}}} \\ \\ \purple{\tt{\therefore{First \ term \ is \ 60.}}$