A two-digit number is formed by either subtracting 16 from eight times the sum of the digits or by adding 20 to 22 times the difference of the digits. Find the number.

Question

zepdrix · Answer

@ganeshie8 @wio @dan815 
Really cool looking problem. I can't seem to figure it out though.

anonymous · Answer

the answer happens to be 64, but i can't make a linear equation that supports it.

ganeshie8 · Answer

i remember @SithsAndGiggles doing this problem few days back...

zepdrix · Answer

I was trying to approach it like this...
Yah maybe this will work,$$\Large\rm \{xy\}=8(x+y)-16$$$$\Large\rm \{xy\}=22(x-y)+20$$Where $\Large\rm \{xy\}$ is some 2 digit number.

Subtracting the first from the second equation gives us:$$\Large\rm 0=22x-22y-8x-8y+36$$So we have -30y.
If the y is the one's place, then it's the same as -3x.
$$\Large\rm 0=22x-8x-3x+36\qquad\to\qquad x\approx 3.27...$$Hmm doesn't seem to be working out :[
Yah my approach is probably flawed somewhere in there...

aum · Answer

{xy} = 10x + y

anonymous · Answer

8(10x + y) - 16 and 22(10x - y) +20 are the two equations i've formed... i'm always getting -7x + 15y = 18

aum · Answer

From zepdrix equations:
10x + y = 8x + 8y - 16
2x - 7y = -16  --- (3)

10x + y = 22x - 22y + 20
-12x + 23y = 20 ---- (4)
 12x  - 42y = -96  ( (3) * 6 )
add:
         -19y = -96
y = 4
put y = 4 in (3)
2x - 28 = -16
2x = 28-16 = 12
x = 6

The number is {xy} = 64

ganeshie8 · Answer

nice :)

anonymous · Answer

thanks aum :)

aum · Answer

You are welcome.