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anonymous
 one year ago
The digits of a positive twodigit integer N are interchanged to form integer K. Find all possibilities for N under the conditions described: The sum of K and twice N is less than 60.
How do I write an equation for this?
anonymous
 one year ago
The digits of a positive twodigit integer N are interchanged to form integer K. Find all possibilities for N under the conditions described: The sum of K and twice N is less than 60. How do I write an equation for this?

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freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[26 \text{ is a two digit number } \\ \text{ another way to express this is } 2 \cdot 10 +6 \\ \text{ So say } N=xy \text{ where } x \text{ is in the tens digit } \\ \text{ and } y \text{ is in the one's digit } \\ \text{ So } N=10x+y\] (by the way this xy I have written for N doesn't mean x and y multiplied; it is just the digits of N)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1So can you write what K would look like

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so you have N=10x+y and K=10y+x and you are given K+2N<60

freckles
 one year ago
Best ResponseYou've already chosen the best response.1just plug in your K and your N and combine like terms

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and if you want to find N check a few pairs for (x,y)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.010y+x + 2(10x+y) <60 10y+x+20x+2y < 60 12y+ 21x < 60 21x<6012y x= 60/21  12/21y

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[x<\frac{60}{21}\frac{12}{21} y \text{ though I probably would leave \it like } \\ 12y+21x<60\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so N is two digits and N in digit form looks like N=xy we don't want x to be 0 because basically that would mean N is a one digit number

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so (1,0) would be the first pair I look at

freckles
 one year ago
Best ResponseYou've already chosen the best response.1then (1,1) and I would keep doing this to til I bust (you know go over 60)

freckles
 one year ago
Best ResponseYou've already chosen the best response.121(1)+12(0)=21<60 so N=10 is good 21(1)+12(1)=21+12=33<60 so N=11 is good

anonymous
 one year ago
Best ResponseYou've already chosen the best response.021(1)+12(2)= 45 < 60 21(1)+12(3)= 57<60 21(1)+12(4)= 69>60

freckles
 one year ago
Best ResponseYou've already chosen the best response.1ok but I don't think that is all

freckles
 one year ago
Best ResponseYou've already chosen the best response.1we can look at N=20,21,22

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and 3something wouldn;t work because 21(3)=63

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I see how to do this now. Thank you sooo much! I was stuck on this yesterday because I divided by 21 and kept getting decimals.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1np i'm just glad my way wasn't too long :p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's a good way. Thank you again!
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