1. ## Proportional Increase?

I'm not sure if this should be here or in geometry, but...
I have two lines A and B, and I know their length. Thus I can get A + B = L0. I now have L1. How do I find the length of A and B such that A/B remains the same?
Another way to look at it is that all the following must be true, with A, B, and F all known and I'm looking for C and D.
A + B = N
A / B = R
C + D = F
C / D = R

2. ## Re: Proportional Increase?

Originally Posted by OddGamer
I'm not sure if this should be here or in geometry, but...
I have two lines A and B, and I know their length. Thus I can get A + B = L0. I now have L1. How do I find the length of A and B such that A/B remains the same?
I'm not clear what you are asking. You have A and B such that A+ B= L0. Then you say "I now have L1." What does that mean? Are you saying that you want two additional A and B such that there sum is L1? If that is the situation then it would be better to call the first two A1 and B1 and the other two A2 and B2 since they are different numbers. So we have A1+ B1= L0, A2+ B2= L1, and A1/B1= A2/B2. Now that is only three equations in two unknowns so there are many solutions.

Another way to look at it is that all the following must be true, with A, B, and F all known and I'm looking for C and D.
A + B = N
A / B = R
C + D = F
C / D = R
I should have read the second paragraph before I responded to the first! Yes, here N and F are "given" so known constants but R, if I am reading this correctly, is not given. You can think of this as four equations in the five "unknowns", A, B, C, D, and R or combine A/B= R and C/D= R into the single equation A/B= C/D. That, again, gives three equations in four unknowns. You can solve for all of the other unknowns in terms of any one.

3. ## Re: Proportional Increase?

You have a system of equations:

$C+D = F$ and $\dfrac{C}{D} = R$

In the second equation, solve for $C$ by multiplying both sides by $D$: $C = RD$

Plug that into the first equation:

$RD + D = F$

Solve for $D$:

$D = \dfrac{F}{R+1}$

Plug that back in to find $C$:

$C = \dfrac{RF}{R+1}$