Answer to Question #235812 in Algebra for Ahmed

Question

24 pairwise different positive integer numbers are written on the board. Their mean value is equal to 38. Let M be the smallest of these numbers. Find the largest possible value of M.

Answer 1

given

mean value of these integers=38

total number of integers=24

mean value=sum of numbers$\div$ total number of integers

38=sum of numbers$\div$ 24

sum of numbers=$38\times 24$

As we sum in A.P

$s_n=\frac{n}{2}[2a+(n-1)d]\\n=24\\s_n=38\times 24\\d=1\space (unique \space difference)$

$38\times24=\frac{24}{2}[2a+(24-1)1]\\38=\frac{1}{2}[2a+23]\\76=2a+23\\2a=53\\a=26.5$

So smallest of tese numbers is 26.5 so largest possible vale of M is 26.5