Question

If (r+s)/r=3 and (t+r)/t=5, what is the value of s/t?

Answer 1

id rewrite it\[\frac{ r }{ r }+\frac{ s }{ r } = 5 \rightarrow \frac{ t }{ t }+\frac{ r }{ t }=5\]

Answer 2

does that give you enough of a hint to solve it

Answer 3

I dont understand the way you wrote it

Answer 4

you see that s/r = 4 and r/t = 4

Answer 5

ok do you agree that... hold on

Answer 6

I think you had a typo because the first one is equal to 3, not 5

Answer 7

\[\frac{ x+y }{ z }\rightarrow \frac{ x }{ z }+\frac{ y }{ z }\]these are equal

and deybow is correct I did make a typo. The first is equal to 3

Answer 8

Also, I solved it somewhat differently. I just started right away with solving each equation for r because they both have an r in them. That way, once you do this, you can set them equal to each other and then solve for s/t.

Answer 9

so, you now have s/r=2 and r/t=4

Answer 10

What do i do after i get s/r=2 and r/t=4

Answer 11

I was going to do what @Deybow said. solve for r and set them equal

Answer 12

@Deybow I simplified it first just to make it less messy and hopefully easier to explain. but you are right

Answer 13

yeah, that's what I thought. It just seems like an extra step to me, but it all depends on how you think.

Answer 14

solving for r we have s/2=r and 4t=r

Answer 15

It is extra but you have to multiply by r then subtract r then divide by its coefficient. Hmm I guess in retrospec it wasnt that messy

Answer 16

Once you solve each for r you can set them equal and solve for s/t.

s/2=4t --> s/2t=4 --> s/t=8

Answer 17

haha yeah

Answer 18

Do you also see @Deybow 's way of solving it.both are fine, whatever you are most comfortable with. Good luck

Answer 19

I can show my work if you want me to.

(r+s)/r=3
r+s=3r
s=2r
r=s/2

(t+r)/t=5
t+r=5t
r=4t

r=s/2 and r=4t
therefore, s/2=4t
s=8t
s/t=8

Answer 20

Thank you both