The digits of a positive two-digit 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

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- freckles

\[26 \text{ is a two digit number } \\ \text{ another way to express this is } 2 \cdot 10 +6 \\ \text{ So say } N=xy \text{ where } x \text{ is in the tens digit } \\ \text{ and } y \text{ is in the one's digit } \\ \text{ So } N=10x+y\]
(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

So can you write what K would look like

- anonymous

k = 10y + x

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- freckles

great

- freckles

so you have N=10x+y and K=10y+x
and you are given K+2N<60

- freckles

just plug in your K and your N
and combine like terms

- freckles

and if you want to find N
check a few pairs for (x,y)

- anonymous

10y+x + 2(10x+y) <60
10y+x+20x+2y < 60
12y+ 21x < 60
21x<60-12y
x= 60/21 - 12/21y

- anonymous

Is this correct?

- freckles

\[x<\frac{60}{21}-\frac{12}{21} y \text{ though I probably would leave \it like } \\ 12y+21x<60\]

- freckles

\[21x+12y<60\]

- freckles

so 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

so (1,0) would be the first pair I look at

- freckles

then (1,1)
and I would keep doing this to til I bust (you know go over 60)

- freckles

21(1)+12(0)=21<60 so N=10 is good
21(1)+12(1)=21+12=33<60 so N=11 is good

- freckles

see if 12 works

- anonymous

21(1)+12(2)= 45 < 60
21(1)+12(3)= 57<60
21(1)+12(4)= 69>60

- freckles

ok but I don't think that is all

- freckles

we can look at N=20,21,22

- anonymous

20 and 21 work

- freckles

and 3something wouldn;t work because 21(3)=63

- freckles

so now we are done

- anonymous

I 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

np
i'm just glad my way wasn't too long :p

- anonymous

It's a good way. Thank you again!

- freckles

np

Looking for something else?

Not the answer you are looking for? Search for more explanations.