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nlincoln · Dec 28, 2010, 03:20 PM

. At a diving competition, John's first dive received seven scores that averaged 8.0. To calculate his final score for the dive, the highest and lowest scores were removed and the average was then taken of the five remaining scores. If his final score was 7.7, what was the sum of the two removed scores?

Capuchin · Dec 28, 2010, 04:01 PM

How far have you gotten? Have you formulated an equation to solve?

nlincoln · Dec 29, 2010, 12:41 PM

I have got nothing so far.

Capuchin · Dec 29, 2010, 01:31 PM

OK so we write the equation for the mean of 7 variables:

$\mu_{initial} = \frac{s_{1}+s_{2}+s_{3}+s_{4}+s_{5}+s_{6}+s_{7}}{7 }$

We also can write an equation for the altered total with the highest and lowest ( $s_{7}$ and $s_{1}$ ) scores removed:

$\mu_{altered} = \frac{s_{2}+s_{3}+s_{4}+s_{5}+s_{6}}{5}$

Can you see where to go from here (hint, you can substitute in values for $\mu_{initial}$ and $\mu_{final}$ , do some rearranging of the second equation, and then substitute the second equation into the first.)

Let me know how far you get and if you have further questions