Question 771775

The average (arithmetic mean) of the numbers {{{12}}}, {{{28}}}, {{{16}}}, and {{{x}}} is:

{{{(12+28+16+x)/4}}}

given that the average is between {{{22}}} and {{{24}}}, inclusive-means{{{22<=x<=24}}}; so, we have


{{{22<=(12+28+16+x)/4<=24}}}......solve for {{{x}}}

{{{22<=(56+x)/4<=24}}}....multiply by {{{4}}}

{{{22*4<=4*(56+x)/4<=24*4}}}

{{{88<=56+x<=96}}}....subtract {{{56}}}

{{{88-56<=56-56+x<=96-56}}}

{{{32<=x<=40}}}

so, since {{{32<=x}}}, the least possible value of {{{x}}} is {{{32}}}


check:

{{{(12+28+16+x)/4}}}.....plug in {{{x=32}}}

{{{(12+28+16+32)/4=88/4=22}}} and {{{22<=22<=24}}}