Can anyone me with this division and remainder problem?

AI Thread Summary
The discussion revolves around a division and remainder problem posed by a music teacher seeking assistance. The equation presented is unclear, but it is interpreted as "w divided by 81 equals 26 remainder 3." To solve for w, the equation can be rewritten as (w / 81) = 26 + (3/81). Multiplying both sides by 81 yields the value of w. The conversation emphasizes clarifying notation for accurate problem-solving.
Victoriacv
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Is there any chance someone can help me solve this? Music teacher with absolutely no idea how to solve this. Thanl you so much.

? w!81 = 26r3 (the goal is to find the first number, and explain how you figured it out)
 
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Can you explain the notation? It is not standard mathematical notation.
 
Perhaps @Victoriacv meant to type: w divided by 81 equals 26 remainder 3. If that is the case, then you can rewrite as (w / 81) = 26 + (3/81), then multiply both sides by 81 and get the value of w.
 
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I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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