If X and Y are different positive integers and 3x+y=17, the difference between the largest possible value of y and the smallest possible value of y is?

Question

anonymous · Answer

i think its infinite but idk for sure, maybe ask someone like... ummmm.... @wio @whpalmer4 or someone im so sorry

anonymous · Answer

do i message him/her?

anonymous · Answer

yeah ig ^_^

anonymous · Answer

um how long will it take for them to reply?

anonymous · Answer

sorry i couldnt be more help... idk... they are online i believe

anonymous · Answer

Oh its, thank for telling me who to ask :)

anonymous · Answer

@torchriswil

anonymous · Answer

yvw ^_^

whpalmer4 · Answer

$$3x+y=17$$Solve for $y$, what do you get?

anonymous · Answer

y=-3x+17

whpalmer4 · Answer

Okay, can we get y = 1 and still have x be a positive integer?

anonymous · Answer

no

anonymous · Answer

wait actually yes

whpalmer4 · Answer

Really, what value will x have in that case?

anonymous · Answer

wait wait wait noo i mean no

whpalmer4 · Answer

Okay, that's better :-) what's the smallest value we can have for y?

anonymous · Answer

2

whpalmer4 · Answer

Very good.  What's the largest value we can have?

whpalmer4 · Answer

Why don't you try finding the value of $x$ for $y = 3, 4, 5, $etc. and see if you see a pattern developing...

anonymous · Answer

its subtracting by 3

whpalmer4 · Answer

Okay.  so what is the largest value of y we can have and still have a positive value of x?

whpalmer4 · Answer

might try plotting x,y on a graph...

anonymous · Answer

5

anonymous · Answer

sorry i am stumped i would graph it for you but i dont know what the second equation is

whpalmer4 · Answer

y = 5?  are you sure about that?

whpalmer4 · Answer

there's only one equation...

$$y = -3x+17$$

We want the biggest value of $y$ that is a positive integer where $x$ is also a positive integer.

anonymous · Answer

no wait its not 5

whpalmer4 · Answer

Does $$y = -3x+17$$remind you of the equation for a line in slope-intercept form, perhaps?

anonymous · Answer

yes

anonymous · Answer

is it y=14

whpalmer4 · Answer

ding ding ding!  we have a winnah!

So what is the maximum difference between the smallest possible value of $y$ and the largest possible value?

anonymous · Answer

12

anonymous · Answer

i know this but since there is no second equation their is no point in it  and there is no value for x witch would make the problem super easy but i honestly don't know where to start do you @whpalmer4..

whpalmer4 · Answer

Here's a graph of the line produced by that equation.  I have a vertical line at each positive integer value of $x$ and a horizontal line at each positive integer value of $y$ that matches with one of those values of $x$.

whpalmer4 · Answer

It's clear that we can't get a bigger value of $y$ than 14, or a smaller one than 2, agreed?

anonymous · Answer

mhm

anonymous · Answer

no the graph is infinite so it could go on forever but it would go into negative numbers i see the largest is 14 but the smallest is not 2

anonymous · Answer

correct?

whpalmer4 · Answer

Remember, both $x$ and $y$ must be positive integers!

anonymous · Answer

Yea i know

anonymous · Answer

oh then yes you are correct i over looked the fact it was positive this was what confused me im sorry and ys the answer is 12

whpalmer4 · Answer

if we went to x=6, then y = -3(6)-17 = -1, and that's not a positive integer.  

Glad we're all in agreement.  I think this horse, if not dead, is at least going to stay down on the ground until we're all out of sight :-)

anonymous · Answer

whpalmer4 may you help me with another question?

whpalmer4 · Answer

post it and tag me, I need to help another guy who did so while I was working this one with you.

anonymous · Answer

nice idiom

anonymous · Answer

who do i tag you?

anonymous · Answer

just write @whpalmer4 under your question like i just did

anonymous · Answer

oh ok thank you

anonymous · Answer

no problem :)