OpenStudy (calculusxy):

How many two digit whole numbers are increased by 18 when their digits are reversed?

3 years ago
OpenStudy (calculusxy):

Hello ganeshie8. Long time since we have seen each other. :)

3 years ago
OpenStudy (bibby):

I don't really know math so I think my approach would be a simple and quick program.

3 years ago
ganeshie8 (ganeshie8):

:) lets write an equation in powers of 10

3 years ago
OpenStudy (calculusxy):

Ok

3 years ago
ganeshie8 (ganeshie8):

say the two digit number = \(xy = 10^1x+10^0y = 10x+y\) then, its reverse wud be : \(yx = 10^1y+10^0x = 10y+x\)

3 years ago
ganeshie8 (ganeshie8):

\(10x + y = 10y-x+18\) solve it in whole numbers :)

3 years ago
OpenStudy (calculusxy):

Wait. How did you get this equation?

3 years ago
ganeshie8 (ganeshie8):

typo : \(10x + y = 10y \color{red}{+}x+18\)

3 years ago
ganeshie8 (ganeshie8):

How many two digit whole numbers are increased by 18 when their digits are reversed so the equation is incorrect still :|

3 years ago
ganeshie8 (ganeshie8):

lets fix it :- reversed number = original number + 18 \(10y + x = 10x +y + 18\)

3 years ago
ganeshie8 (ganeshie8):

see if that makes sense; we can go wid solving the equation...

3 years ago
OpenStudy (calculusxy):

So in short, you just reversed the position of x and y to be with 10 right? And then you just added 18. But why did you do it only to the right equation, not the left?

3 years ago
ganeshie8 (ganeshie8):

okay, lets see if i understood ur q correctly... take some number :- \(2013\) can you write it in powers of 10 ? :)

3 years ago
OpenStudy (calculusxy):

I am not too sure with this. But I will use my prior knowledge for this. 2.013 x 10^3 20.13 x 10^2 201.3 x 10^1 2013 x 10^0

3 years ago
ganeshie8 (ganeshie8):

thats right, but i was asking even more simpler question; we can express \(2013\) in sum of powers as below :- \(2013\) \(2\) thousands = \(2\times 10^3\) \(0\) hundreds= \(0\times 10^2\) \(1\) tens = \(1\times 10^1\) \(3\) ones = \(3\times 10^0\) ---------------------------------- \(2013 = 2 \times 10^3 + 0 \times 10^2 + 1 \times 10^1 + 3 \times 10^0\)

3 years ago
OpenStudy (calculusxy):

Yes :)

3 years ago
ganeshie8 (ganeshie8):

cool :) so a number \(xy\) can be expressed as \(x \times 10^1 + y \times 10^0 \)

3 years ago
OpenStudy (calculusxy):

Makes sense. What is the next step?

3 years ago
ganeshie8 (ganeshie8):

write its reverse also in powers of 10 and form an equation

3 years ago
OpenStudy (calculusxy):

Couldn't get you there. Can you explain quite more of what you meant?

3 years ago
ganeshie8 (ganeshie8):

\(xy = x \times 10^1 + y \times 10^0 = 10y + x\) reverse of \(xy = yx = y\times 10^1 + x \times 10^0 = 10y+x\)

3 years ago
ganeshie8 (ganeshie8):

yahh, wid me so far ?

3 years ago
OpenStudy (calculusxy):

Why did u put 10y though and then plus x? (Sorry for asking u so many question :/)

3 years ago
ganeshie8 (ganeshie8):

whew ! typo again, it should be :- \(xy = x \times 10^1 + y \times 10^0 = 10x + y\) reverse of \(xy = yx = y\times 10^1 + x \times 10^0 = 10y+x\)

3 years ago
ganeshie8 (ganeshie8):

see if it looks okay now ?

3 years ago
OpenStudy (calculusxy):

Yes now makes sense :)

3 years ago
ganeshie8 (ganeshie8):

nice :) next we're asked to find numbers such that reverse is 18 more than the original :- reversed number = original number + 18 \(10y+x=10x+y+18\)

3 years ago
ganeshie8 (ganeshie8):

rearrange and simplify a bit...

3 years ago
OpenStudy (calculusxy):

Ok

3 years ago
OpenStudy (calculusxy):

Um.. But can you help me with the rearranging and the simplification though?

3 years ago
OpenStudy (anonymous):

let the no. at unit place=x no.at ten's place=y no=10y+x according to the given condition 10x+y=10y+x+18 9x=9y+18 x=y+2 now y>0 \[0 \le x \le 9 also x>y as x=y+2 if we take 1,2,3,4,5,6,7 ,x=3,4,5,6,,7,8,9 respectively\] so nos are 13,24,,35,46,57,68,79 Hence they are 7 in no.

3 years ago
OpenStudy (calculusxy):

What is no.?

3 years ago
OpenStudy (anonymous):

you can see thee are seven two digit nos.

3 years ago
OpenStudy (calculusxy):

And surjithayer how do you get x=y+2

3 years ago
OpenStudy (anonymous):

divide by 9,9x=9y+18

3 years ago
OpenStudy (anonymous):

note y >0 if y=0 then it is not a two digit no.

3 years ago