Hi was wondering if there's anyway you can figure out the value of two terms when you're giving the average of the set they're in, and the values of the other numbers in the set. Based on a revision question I'm trying to figure out that goes like: "The integers from 1 to 9 are written on a white board. When m 8s and n 9s are added to the list, their mean value is 7.3. What is m+n" I dunno if maybe its a misprint and I don't have enough information since I can get as far as generating the formula 7m+17n=207, but cannot figure out how to generate another formula since I need two as there are two unknowns. FYI, the answer at the back of the book is 21, making m=15, and n=6, but I need to figure out how to get that answer without first knowing m+n=21.
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Big hint: $m$ and $n$ are non-negative integers! – Parcly Taxel Dec 03 '17 at 16:10
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You could use some elementary number theory.
$m = \frac {207-17n}7$
You need to find for what value of $n$, $7|(207-17n)$
Sp, $207 - 17n \equiv 0 \mod 7 $
$4n\equiv3 \mod 7$
$\implies n \equiv 6 \mod7$
So, $n=6 + 7k$
Now you can check for $n=6, 13, ...$
Maadhav
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Well, sure, but I figured the OP would more easily see the other one from the given equation. Up to you, obviously. – rogerl Dec 03 '17 at 16:17
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I think you can't be certain. Given $s $ being the sum of the rest, $n $ the size of the set (I assume that's given too) an $m $ the mean of the set, we want to know $a $ and $b $ but only know the equality
$$\frac {s+a+b}{n}=m $$
One equality and two variables means there is no unique solution.
SK19
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