Math Is Fun Forum

simone

Member

Registered: 2007-10-05

Posts: 19

arithmetics

hi, could you please explain to me the following problem and the reasoning behind the solution? thank you!

5 numbers have an average (arithmetic mean) of 124 and a median of 140. What is the max possible value of the lowest number?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: arithmetics

Let the five numbers, arranged from smallest to the largest in value, be a, b, 140, c, d. We have

And we have

Thus the maximum possible value of the lowest number is 120.

Last edited by JaneFairfax (2007-10-09 02:46:56)

simone

Member

Registered: 2007-10-05

Posts: 19

Re: arithmetics

thank you Jane, I understood every step. Do you have any idea as to why the book I'm practicing on posts 100 and not 120 as the answer?
thank you.:/

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: arithmetics

Sorry, I made a slight mistake in my working.

i.e.

Adding up the above four inequalities

So the book is right.

Last edited by JaneFairfax (2007-10-09 04:25:41)

simone

Member

Registered: 2007-10-05

Posts: 19

Re: arithmetics

thank you so much.

Last edited by simone (2007-10-09 04:51:32)