Algebra 1b - System of equations

AI Thread Summary
The discussion revolves around solving a problem involving a two-digit number where the sum of its digits is 7, and reversing the digits increases the number by 27. Participants express confusion over the wording related to reversing the digits. One user illustrates the concept with an example, demonstrating how reversing affects the value of the number. This clarification helps others understand the problem better. Ultimately, the key takeaway is the relationship between the digits and how their positions influence the overall value.
lederhosen
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Homework Statement



The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number

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I Don't understand when they say the digits are reversed, i have done these problems many times before. but i don't understand the wording...

Homework Equations


X+Y=7
(help)

The Attempt at a Solution



I need more info to solve...
 
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lederhosen said:

Homework Statement



The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number

------------
I Don't understand when they say the digits are reversed, i have done these problems many times before. but i don't understand the wording...


Homework Equations


X+Y=7
(help)

The Attempt at a Solution



I need more info to solve...

Yeah, that is confusing, but I think I see what they are asking.

Say the original number was 43, so the sum of 4+3 = 7.

Now reverse the two digits to make 34. Well, that decreased the value of the number by 9, so 43 is not the right answer. But you see how it goes now?
 
oh i see i was looking at it completely wrong I really appreciate it
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

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
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Thread 'Greatest possible value of a constant in polynomial'

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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