Divide me by 7, the remainder is 5. Divide me by 3,
the remainder is 1 and my quotient is 2 less than 3
times my previous quotient. What number am I?

Question

Vocaloid · Answer

let's let the mystery number be y
the first quotient can be x
the second quotient can be z

y/7 = x + 5
y/ 3 = z + 1

"second quotient is 2 less than 3
times my previous quotient"

z = 3x - 2

plug this into z into the second equation to make both equations in terms of x and y and then solve by setting up a system of equations and using elimination to find y

Vocaloid · Answer

sorry if this is taking a while I'm on mod duty and I'm dealing with trolls

candygirl220 · Answer

its okay

Vocaloid · Answer

yeah I got 168 too gj

candygirl220 · Answer

thank you!

Vocaloid · Answer

hm now that I'm double checking it it doesn't quite work

let me redo it ;_;

candygirl220 · Answer

ok

Vocaloid · Answer

sorry I'm really drawing a blank here as to how to do this systematically @563blackghost @sillybilly123

563blackghost · Answer

Are you finding y specifically or each solution? There three since there are three variables.

Vocaloid · Answer

it's just asking for the initial number y so just y

563blackghost · Answer

well I got 168 as well O.O

Vocaloid · Answer

yeah the problem is that 168 doesn't satisfy the first condition (it's divisible by 7 so no remainder) ;_; I don't know how to set up the equation so that x and z are integers only

563blackghost · Answer

hmmm

Vocaloid · Answer

I have a friend who knows a bit of discrete math, I'm going to ask if she can help ;; you can solve this using modulus operators

candygirl220 · Answer

ok

dude · Answer

http://www.wolframalpha.com/input/?i=solve+x+mod+7+%3D+5,+x+mod+3+%3D+1

dude · Answer

Possible numbers, 19 or 40

Vocaloid · Answer

40 works, I don't think 19 satisfies the second condition though

dude · Answer

Yep
13 = 3*5 - 2

sillybilly123 · Answer

$n \equiv_7 5 \implies n = 7 \alpha + 5$

$n \equiv_3 1 \implies n = 3 \beta + 1$

For the weirder bit ...."and my quotient is 2 less than 3
times my previous quotient".... I guess that means

$\beta = 3 \alpha - 2$

Which means that:

$ 7 \alpha + 5 = 3 (3 \alpha - 2) + 1$

Or $\alpha = 5$ so $n = 40$

candygirl220 · Answer

thank you everyone who helped!